Precalculus Examples

$x^{2} - 2 x - 4 y - 7 = 0$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 1.1.1

Subtract $x^{2}$ from both sides of the equation.

$- 2 x - 4 y - 7 = - x^{2}$

Step 1.1.2

Add $2 x$ to both sides of the equation.

$- 4 y - 7 = - x^{2} + 2 x$

Step 1.1.3

Add $7$ to both sides of the equation.

$- 4 y = - x^{2} + 2 x + 7$

Step 1.2

Divide each term in $- 4 y = - x^{2} + 2 x + 7$ by $- 4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 4 y = - x^{2} + 2 x + 7$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- x^{2}}{- 4} + \frac{2 x}{- 4} + \frac{7}{- 4}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- x^{2}}{- 4} + \frac{2 x}{- 4} + \frac{7}{- 4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x^{2}}{- 4} + \frac{2 x}{- 4} + \frac{7}{- 4}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{x^{2}}{4} + \frac{2 x}{- 4} + \frac{7}{- 4}$

Step 1.2.3.1.2

Cancel the common factor of $2$ and $- 4$ .

Tap for more steps...

Step 1.2.3.1.2.1

Factor $2$ out of $2 x$ .

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

Step 1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.2.1

Factor $2$ out of $- 4$ .

$y = \frac{x^{2}}{4} + \frac{2 x}{2 \cdot - 2} + \frac{7}{- 4}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{x^{2}}{4} + \frac{2 x}{2 \cdot - 2} + \frac{7}{- 4}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{x^{2}}{4} + \frac{x}{- 2} + \frac{7}{- 4}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{x^{2}}{4} - \frac{x}{2} + \frac{7}{- 4}$

Step 1.2.3.1.4

Move the negative in front of the fraction.

$y = \frac{x^{2}}{4} - \frac{x}{2} - \frac{7}{4}$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

Reorder terms.

$y = \frac{1}{4} x^{2} - (\frac{1}{2} x) - \frac{7}{4}$

Step 4

Remove parentheses.

$y = \frac{1}{4} x^{2} - \frac{1}{2} x - \frac{7}{4}$

Step 5