Solve by Completing the Square x^2+16x+64=0

$x^{2} + 16 x + 64 = 0$

Step 1

Subtract $64$ from both sides of the equation.

$x^{2} + 16 x = - 64$

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 $b$ .

${(\frac{b}{2})}^{2} = {(8)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 16 x + {(8)}^{2} = - 64 + {(8)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $8$ to the power of $2$ .

$x^{2} + 16 x + 64 = - 64 + {(8)}^{2}$

Simplify the right side.

Simplify $- 64 + {(8)}^{2}$ .

Raise $8$ to the power of $2$ .

$x^{2} + 16 x + 64 = - 64 + 64$

Add $- 64$ and $64$ .

$x^{2} + 16 x + 64 = 0$

Step 5

Factor the perfect trinomial square into ${(x + 8)}^{2}$ .

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

Step 6

Solve the equation for $x$ .

Set the $x + 8$ equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$