Solve by Completing the Square 2x^2+16x=-18

$2 x^{2} + 16 x = - 18$

Step 1

Divide each term in $2 x^{2} + 16 x = - 18$ by $2$ and simplify.

Divide each term in $2 x^{2} + 16 x = - 18$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{16 x}{2} = \frac{- 18}{2}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{16 x}{2} = \frac{- 18}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{16 x}{2} = \frac{- 18}{2}$

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

Factor $2$ out of $16 x$ .

$x^{2} + \frac{2 (8 x)}{2} = \frac{- 18}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x^{2} + \frac{2 (8 x)}{2 (1)} = \frac{- 18}{2}$

Cancel the common factor.

$x^{2} + \frac{2 (8 x)}{2 \cdot 1} = \frac{- 18}{2}$

Rewrite the expression.

$x^{2} + \frac{8 x}{1} = \frac{- 18}{2}$

Divide $8 x$ by $1$ .

$x^{2} + 8 x = \frac{- 18}{2}$

Simplify the right side.

Divide $- 18$ by $2$ .

$x^{2} + 8 x = - 9$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(4)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 8 x + {(4)}^{2} = - 9 + {(4)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $4$ to the power of $2$ .

$x^{2} + 8 x + 16 = - 9 + {(4)}^{2}$

Simplify the right side.

Simplify $- 9 + {(4)}^{2}$ .

Raise $4$ to the power of $2$ .

$x^{2} + 8 x + 16 = - 9 + 16$

Add $- 9$ and $16$ .

$x^{2} + 8 x + 16 = 7$

Step 5

Factor the perfect trinomial square into ${(x + 4)}^{2}$ .

${(x + 4)}^{2} = 7$

Step 6

Solve the equation for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 4 = \pm \sqrt{7}$

Subtract $4$ from both sides of the equation.

$x = \pm \sqrt{7} - 4$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{7} - 4$

Decimal Form:

$x = - 1.35424868 \dots, - 6.64575131 \dots$

Solve by Completing the Square 2x^2+16x=-18

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