Algebra Examples

$y = \frac{1}{4} {(x - 3)}^{2}$ $3 x - 2 y = 13$

Step 1

Simplify $\frac{1}{4} \cdot {(x - 3)}^{2}$ .

Tap for more steps...

Step 1.1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$y = \frac{1}{4} \cdot ((x - 3) (x - 3))$

$3 x - 2 y = 13$

Step 1.2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$y = \frac{1}{4} \cdot (x (x - 3) - 3 (x - 3))$

$3 x - 2 y = 13$

Step 1.2.2

Apply the distributive property.

$y = \frac{1}{4} \cdot (x \cdot x + x \cdot - 3 - 3 (x - 3))$

$3 x - 2 y = 13$

Step 1.2.3

Apply the distributive property.

$y = \frac{1}{4} \cdot (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

$3 x - 2 y = 13$

$y = \frac{1}{4} \cdot (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

$3 x - 2 y = 13$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x$ by $x$ .

$y = \frac{1}{4} \cdot (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3)$

$3 x - 2 y = 13$

Step 1.3.1.2

Move $- 3$ to the left of $x$ .

$y = \frac{1}{4} \cdot (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3)$

$3 x - 2 y = 13$

Step 1.3.1.3

Multiply $- 3$ by $- 3$ .

$y = \frac{1}{4} \cdot (x^{2} - 3 x - 3 x + 9)$

$3 x - 2 y = 13$

$y = \frac{1}{4} \cdot (x^{2} - 3 x - 3 x + 9)$

$3 x - 2 y = 13$

Step 1.3.2

Subtract $3 x$ from $- 3 x$ .

$y = \frac{1}{4} \cdot (x^{2} - 6 x + 9)$

$3 x - 2 y = 13$

$y = \frac{1}{4} \cdot (x^{2} - 6 x + 9)$

$3 x - 2 y = 13$

Step 1.4

Apply the distributive property.

$y = \frac{1}{4} x^{2} + \frac{1}{4} \cdot (- 6 x) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Combine $\frac{1}{4}$ and $x^{2}$ .

$y = \frac{x^{2}}{4} + \frac{1}{4} \cdot (- 6 x) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.5.2.1

Factor $2$ out of $4$ .

$y = \frac{x^{2}}{4} + \frac{1}{2 (2)} \cdot (- 6 x) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.2.2

Factor $2$ out of $- 6 x$ .

$y = \frac{x^{2}}{4} + \frac{1}{2 (2)} \cdot (2 (- 3 x)) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.2.3

Cancel the common factor.

$y = \frac{x^{2}}{4} + \frac{1}{2 \cdot 2} \cdot (2 (- 3 x)) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.2.4

Rewrite the expression.

$y = \frac{x^{2}}{4} + \frac{1}{2} \cdot (- 3 x) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

$y = \frac{x^{2}}{4} + \frac{1}{2} \cdot (- 3 x) + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.3

Combine $- 3$ and $\frac{1}{2}$ .

$y = \frac{x^{2}}{4} + \frac{- 3}{2} x + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.4

Combine $\frac{- 3}{2}$ and $x$ .

$y = \frac{x^{2}}{4} + \frac{- 3 x}{2} + \frac{1}{4} \cdot 9$

$3 x - 2 y = 13$

Step 1.5.5

Combine $\frac{1}{4}$ and $9$ .

$y = \frac{x^{2}}{4} + \frac{- 3 x}{2} + \frac{9}{4}$

$3 x - 2 y = 13$

$y = \frac{x^{2}}{4} + \frac{- 3 x}{2} + \frac{9}{4}$

$3 x - 2 y = 13$

Step 1.6

Move the negative in front of the fraction.

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - 2 y = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - 2 y = 13$

Step 2

Replace all occurrences of $y$ with $\frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $3 x - 2 y = 13$ with $\frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$ .

$3 x - 2 (\frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $3 x - 2 (\frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4})$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$3 x - 2 \frac{x^{2}}{4} - 2 (- \frac{3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1.1

Factor $2$ out of $- 2$ .

$3 x + 2 (- 1) (\frac{x^{2}}{4}) - 2 (- \frac{3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.1.2

Factor $2$ out of $4$ .

$3 x + 2 \cdot (- 1 \frac{x^{2}}{2 \cdot 2}) - 2 (- \frac{3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.1.3

Cancel the common factor.

$3 x + 2 \cdot (- 1 \frac{x^{2}}{2 \cdot 2}) - 2 (- \frac{3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.1.4

Rewrite the expression.

$3 x - 1 \frac{x^{2}}{2} - 2 (- \frac{3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - 1 \frac{x^{2}}{2} - 2 (- \frac{3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.2.1

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$3 x - 1 \frac{x^{2}}{2} - 2 \frac{- 3 x}{2} - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.2.2

Factor $2$ out of $- 2$ .

$3 x - 1 \frac{x^{2}}{2} + 2 (- 1) (\frac{- 3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.2.3

Cancel the common factor.

$3 x - 1 \frac{x^{2}}{2} + 2 \cdot (- 1 \frac{- 3 x}{2}) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.2.4

Rewrite the expression.

$3 x - 1 \frac{x^{2}}{2} - 1 (- 3 x) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - 1 \frac{x^{2}}{2} - 1 (- 3 x) - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.3

Multiply $- 3$ by $- 1$ .

$3 x - 1 \frac{x^{2}}{2} + 3 x - 2 (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.4.1

Factor $2$ out of $- 2$ .

$3 x - 1 \frac{x^{2}}{2} + 3 x + 2 (- 1) (\frac{9}{4}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.4.2

Factor $2$ out of $4$ .

$3 x - 1 \frac{x^{2}}{2} + 3 x + 2 \cdot (- 1 \frac{9}{2 \cdot 2}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.4.3

Cancel the common factor.

$3 x - 1 \frac{x^{2}}{2} + 3 x + 2 \cdot (- 1 \frac{9}{2 \cdot 2}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.2.4.4

Rewrite the expression.

$3 x - 1 \frac{x^{2}}{2} + 3 x - 1 (\frac{9}{2}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - 1 \frac{x^{2}}{2} + 3 x - 1 (\frac{9}{2}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - 1 \frac{x^{2}}{2} + 3 x - 1 (\frac{9}{2}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.3

Simplify each term.

Tap for more steps...

Step 2.2.1.1.3.1

Rewrite $- 1 \frac{x^{2}}{2}$ as $- \frac{x^{2}}{2}$ .

$3 x - \frac{x^{2}}{2} + 3 x - 1 (\frac{9}{2}) = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.1.3.2

Rewrite $- 1 (\frac{9}{2})$ as $- (\frac{9}{2})$ .

$3 x - \frac{x^{2}}{2} + 3 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - \frac{x^{2}}{2} + 3 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$3 x - \frac{x^{2}}{2} + 3 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 2.2.1.2

Add $3 x$ and $3 x$ .

$- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3

Solve for $x$ in $- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$ .

Tap for more steps...

Step 3.1

Multiply each term in $- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$ by $2$ to eliminate the fractions.

Tap for more steps...

Step 3.1.1

Multiply each term in $- \frac{x^{2}}{2} + 6 x - \frac{9}{2} = 13$ by $2$ .

$- \frac{x^{2}}{2} \cdot 2 + 6 x \cdot 2 - \frac{9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2

Simplify the left side.

Tap for more steps...

Step 3.1.2.1

Simplify each term.

Tap for more steps...

Step 3.1.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.2.1.1.1

Move the leading negative in $- \frac{x^{2}}{2}$ into the numerator.

$\frac{- x^{2}}{2} \cdot 2 + 6 x \cdot 2 - \frac{9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2.1.1.2

Cancel the common factor.

$\frac{- x^{2}}{2} \cdot 2 + 6 x \cdot 2 - \frac{9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2.1.1.3

Rewrite the expression.

$- x^{2} + 6 x \cdot 2 - \frac{9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- x^{2} + 6 x \cdot 2 - \frac{9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2.1.2

Multiply $2$ by $6$ .

$- x^{2} + 12 x - \frac{9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.2.1.3.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$- x^{2} + 12 x + \frac{- 9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2.1.3.2

Cancel the common factor.

$- x^{2} + 12 x + \frac{- 9}{2} \cdot 2 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.2.1.3.3

Rewrite the expression.

$- x^{2} + 12 x - 9 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- x^{2} + 12 x - 9 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- x^{2} + 12 x - 9 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- x^{2} + 12 x - 9 = 13 \cdot 2$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.1.3

Simplify the right side.

Tap for more steps...

Step 3.1.3.1

Multiply $13$ by $2$ .

$- x^{2} + 12 x - 9 = 26$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- x^{2} + 12 x - 9 = 26$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- x^{2} + 12 x - 9 = 26$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.2

Subtract $26$ from both sides of the equation.

$- x^{2} + 12 x - 9 - 26 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.3

Subtract $26$ from $- 9$ .

$- x^{2} + 12 x - 35 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4

Factor the left side of the equation.

Tap for more steps...

Step 3.4.1

Factor $- 1$ out of $- x^{2} + 12 x - 35$ .

Tap for more steps...

Step 3.4.1.1

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 12 x - 35 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.1.2

Factor $- 1$ out of $12 x$ .

$- (x^{2}) - (- 12 x) - 35 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.1.3

Rewrite $- 35$ as $- 1 (35)$ .

$- (x^{2}) - (- 12 x) - 1 \cdot 35 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.1.4

Factor $- 1$ out of $- (x^{2}) - (- 12 x)$ .

$- (x^{2} - 12 x) - 1 \cdot 35 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.1.5

Factor $- 1$ out of $- (x^{2} - 12 x) - 1 (35)$ .

$- (x^{2} - 12 x + 35) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- (x^{2} - 12 x + 35) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.2

Factor.

Tap for more steps...

Step 3.4.2.1

Factor $x^{2} - 12 x + 35$ using the AC method.

Tap for more steps...

Step 3.4.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $35$ and whose sum is $- 12$ .

$- 7, - 5$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.2.1.2

Write the factored form using these integers.

$- ((x - 7) (x - 5)) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- ((x - 7) (x - 5)) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.4.2.2

Remove unnecessary parentheses.

$- (x - 7) (x - 5) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- (x - 7) (x - 5) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$- (x - 7) (x - 5) = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 7 = 0$

$x - 5 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.6

Set $x - 7$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.6.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.6.2

Add $7$ to both sides of the equation.

$x = 7$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$x = 7$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.7

Set $x - 5$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.7.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.7.2

Add $5$ to both sides of the equation.

$x = 5$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$x = 5$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 3.8

The final solution is all the values that make $- (x - 7) (x - 5) = 0$ true.

$x = 7, 5$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

$x = 7, 5$

$y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$

Step 4

Replace all occurrences of $x$ with $7$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $x$ in $y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$ with $7$ .

$y = \frac{{(7)}^{2}}{4} - \frac{3 (7)}{2} + \frac{9}{4}$

$x = 7$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{{(7)}^{2}}{4} - \frac{3 (7)}{2} + \frac{9}{4}$ .

Tap for more steps...

Step 4.2.1.1

Combine fractions.

Tap for more steps...

Step 4.2.1.1.1

Combine the numerators over the common denominator.

$y = \frac{{(7)}^{2} + 9}{4} + \frac{- 3 \cdot 7}{2}$

$x = 7$

Step 4.2.1.1.2

Simplify the expression.

Tap for more steps...

Step 4.2.1.1.2.1

Raise $7$ to the power of $2$ .

$y = \frac{49 + 9}{4} + \frac{- 3 \cdot 7}{2}$

$x = 7$

Step 4.2.1.1.2.2

Add $49$ and $9$ .

$y = \frac{58}{4} + \frac{- 3 \cdot 7}{2}$

$x = 7$

Step 4.2.1.1.2.3

Multiply $- 3$ by $7$ .

$y = \frac{58}{4} + \frac{- 21}{2}$

$x = 7$

$y = \frac{58}{4} + \frac{- 21}{2}$

$x = 7$

$y = \frac{58}{4} + \frac{- 21}{2}$

$x = 7$

Step 4.2.1.2

Simplify each term.

Tap for more steps...

Step 4.2.1.2.1

Cancel the common factor of $58$ and $4$ .

Tap for more steps...

Step 4.2.1.2.1.1

Factor $2$ out of $58$ .

$y = \frac{2 (29)}{4} + \frac{- 21}{2}$

$x = 7$

Step 4.2.1.2.1.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1.2.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 29}{2 \cdot 2} + \frac{- 21}{2}$

$x = 7$

Step 4.2.1.2.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 29}{2 \cdot 2} + \frac{- 21}{2}$

$x = 7$

Step 4.2.1.2.1.2.3

Rewrite the expression.

$y = \frac{29}{2} + \frac{- 21}{2}$

$x = 7$

$y = \frac{29}{2} + \frac{- 21}{2}$

$x = 7$

$y = \frac{29}{2} + \frac{- 21}{2}$

$x = 7$

Step 4.2.1.2.2

Move the negative in front of the fraction.

$y = \frac{29}{2} - \frac{21}{2}$

$x = 7$

$y = \frac{29}{2} - \frac{21}{2}$

$x = 7$

Step 4.2.1.3

Combine fractions.

Tap for more steps...

Step 4.2.1.3.1

Combine the numerators over the common denominator.

$y = \frac{29 - 21}{2}$

$x = 7$

Step 4.2.1.3.2

Simplify the expression.

Tap for more steps...

Step 4.2.1.3.2.1

Subtract $21$ from $29$ .

$y = \frac{8}{2}$

$x = 7$

Step 4.2.1.3.2.2

Divide $8$ by $2$ .

$y = 4$

$x = 7$

$y = 4$

$x = 7$

$y = 4$

$x = 7$

$y = 4$

$x = 7$

$y = 4$

$x = 7$

$y = 4$

$x = 7$

Step 5

Replace all occurrences of $x$ with $5$ in each equation.

Tap for more steps...

Step 5.1

Replace all occurrences of $x$ in $y = \frac{x^{2}}{4} - \frac{3 x}{2} + \frac{9}{4}$ with $5$ .

$y = \frac{{(5)}^{2}}{4} - \frac{3 (5)}{2} + \frac{9}{4}$

$x = 5$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $\frac{{(5)}^{2}}{4} - \frac{3 (5)}{2} + \frac{9}{4}$ .

Tap for more steps...

Step 5.2.1.1

Combine fractions.

Tap for more steps...

Step 5.2.1.1.1

Combine the numerators over the common denominator.

$y = \frac{{(5)}^{2} + 9}{4} + \frac{- 3 \cdot 5}{2}$

$x = 5$

Step 5.2.1.1.2

Simplify the expression.

Tap for more steps...

Step 5.2.1.1.2.1

Raise $5$ to the power of $2$ .

$y = \frac{25 + 9}{4} + \frac{- 3 \cdot 5}{2}$

$x = 5$

Step 5.2.1.1.2.2

Add $25$ and $9$ .

$y = \frac{34}{4} + \frac{- 3 \cdot 5}{2}$

$x = 5$

Step 5.2.1.1.2.3

Multiply $- 3$ by $5$ .

$y = \frac{34}{4} + \frac{- 15}{2}$

$x = 5$

$y = \frac{34}{4} + \frac{- 15}{2}$

$x = 5$

$y = \frac{34}{4} + \frac{- 15}{2}$

$x = 5$

Step 5.2.1.2

Simplify each term.

Tap for more steps...

Step 5.2.1.2.1

Cancel the common factor of $34$ and $4$ .

Tap for more steps...

Step 5.2.1.2.1.1

Factor $2$ out of $34$ .

$y = \frac{2 (17)}{4} + \frac{- 15}{2}$

$x = 5$

Step 5.2.1.2.1.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1.2.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 17}{2 \cdot 2} + \frac{- 15}{2}$

$x = 5$

Step 5.2.1.2.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 17}{2 \cdot 2} + \frac{- 15}{2}$

$x = 5$

Step 5.2.1.2.1.2.3

Rewrite the expression.

$y = \frac{17}{2} + \frac{- 15}{2}$

$x = 5$

$y = \frac{17}{2} + \frac{- 15}{2}$

$x = 5$

$y = \frac{17}{2} + \frac{- 15}{2}$

$x = 5$

Step 5.2.1.2.2

Move the negative in front of the fraction.

$y = \frac{17}{2} - \frac{15}{2}$

$x = 5$

$y = \frac{17}{2} - \frac{15}{2}$

$x = 5$

Step 5.2.1.3

Combine fractions.

Tap for more steps...

Step 5.2.1.3.1

Combine the numerators over the common denominator.

$y = \frac{17 - 15}{2}$

$x = 5$

Step 5.2.1.3.2

Simplify the expression.

Tap for more steps...

Step 5.2.1.3.2.1

Subtract $15$ from $17$ .

$y = \frac{2}{2}$

$x = 5$

Step 5.2.1.3.2.2

Divide $2$ by $2$ .

$y = 1$

$x = 5$

$y = 1$

$x = 5$

$y = 1$

$x = 5$

$y = 1$

$x = 5$

$y = 1$

$x = 5$

$y = 1$

$x = 5$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(7, 4)$

$(5, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(7, 4), (5, 1)$

Equation Form:

$x = 7, y = 4$

$x = 5, y = 1$

Step 8