Algebra Examples

$x^{2} + 16 x = 3$

Step 1

Subtract $3$ from both sides of the equation.

$x^{2} + 16 x - 3 = 0$

Step 2

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1$

$b = 16$

$c = - 3 = 0$

Step 3

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e = 0$

Step 4

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

Tap for more steps...

Step 4.1

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{16}{2 \cdot 1}$

Step 4.2

Cancel the common factor of $16$ and $2$ .

Tap for more steps...

Step 4.2.1

Factor $2$ out of $16$ .

$d = \frac{2 \cdot 8}{2 \cdot 1}$

Step 4.2.2

Cancel the common factors.

Tap for more steps...

Step 4.2.2.1

Factor $2$ out of $2 \cdot 1$ .

$d = \frac{2 \cdot 8}{2 (1)}$

Step 4.2.2.2

Cancel the common factor.

$d = \frac{2 \cdot 8}{2 \cdot 1}$

Step 4.2.2.3

Rewrite the expression.

$d = \frac{8}{1}$

Step 4.2.2.4

Divide $8$ by $1$ .

$d = 8$

Step 5

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps...

Step 5.1

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = - 3 - \frac{16^{2}}{4 \cdot 1}$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify each term.

Tap for more steps...

Step 5.2.1.1

Raise $16$ to the power of $2$ .

$e = - 3 - \frac{256}{4 \cdot 1}$

Step 5.2.1.2

Multiply $4$ by $1$ .

$e = - 3 - \frac{256}{4}$

Step 5.2.1.3

Divide $256$ by $4$ .

$e = - 3 - 1 \cdot 64$

Step 5.2.1.4

Multiply $- 1$ by $64$ .

$e = - 3 - 64$

Step 5.2.2

Subtract $64$ from $- 3$ .

$e = - 67$

Step 6

Substitute the values of $a$ , $d$ , and $e$ into the vertex form ${(x + 8)}^{2} - 67$ .

${(x + 8)}^{2} - 67 = 0$