Solve by Completing the Square x^2+8x=15

$x^{2} + 8 x = 15$

Step 1

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 2

Add the term to each side of the equation.

$x^{2} + 8 x + {(4)}^{2} = 15 + {(4)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

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

$x^{2} + 8 x + 16 = 15 + {(4)}^{2}$

Simplify the right side.

Simplify $15 + {(4)}^{2}$ .

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

$x^{2} + 8 x + 16 = 15 + 16$

Add $15$ and $16$ .

$x^{2} + 8 x + 16 = 31$

Step 4

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

${(x + 4)}^{2} = 31$

Step 5

Solve the equation for $x$ .

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

$x + 4 = \pm \sqrt{31}$

Subtract $4$ from both sides of the equation.

$x = \pm \sqrt{31} - 4$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{31} - 4$

Decimal Form:

$x = 1.56776436 \dots, - 9.56776436 \dots$