Solve by Completing the Square 2x^2+16x-8=0

$2 x^{2} + 16 x - 8 = 0$

Step 1

Add $8$ to both sides of the equation.

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

Step 2

Divide each term in $2 x^{2} + 16 x = 8$ by $2$ and simplify.

Divide each term in $2 x^{2} + 16 x = 8$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{16 x}{2} = \frac{8}{2}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{16 x}{2} = \frac{8}{2}$

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

$x^{2} + \frac{16 x}{2} = \frac{8}{2}$

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

Factor $2$ out of $16 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $8 x$ by $1$ .

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

Simplify the right side.

Divide $8$ by $2$ .

$x^{2} + 8 x = 4$

Step 3

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 4

Add the term to each side of the equation.

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

Step 5

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

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

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

$x^{2} + 8 x + 16 = 4 + 16$

Add $4$ and $16$ .

$x^{2} + 8 x + 16 = 20$

Step 6

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

${(x + 4)}^{2} = 20$

Step 7

Solve the equation for $x$ .

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

$x + 4 = \pm \sqrt{20}$

Simplify $\pm \sqrt{20}$ .

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x + 4 = \pm \sqrt{4 (5)}$

Rewrite $4$ as $2^{2}$ .

$x + 4 = \pm \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$x + 4 = \pm 2 \sqrt{5}$

Subtract $4$ from both sides of the equation.

$x = \pm 2 \sqrt{5} - 4$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{5} - 4$

Decimal Form:

$x = 0.47213595 \dots, - 8.47213595 \dots$

Solve by Completing the Square 2x^2+16x-8=0

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