Solve by Factoring (x+8)^2=64

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

Step 1

Subtract $64$ from both sides of the equation.

${(x + 8)}^{2} - 64 = 0$

Step 2

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

Simplify each term.

Rewrite ${(x + 8)}^{2}$ as $(x + 8) (x + 8)$ .

$(x + 8) (x + 8) - 64 = 0$

Expand $(x + 8) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$x (x + 8) + 8 (x + 8) - 64 = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 + 8 (x + 8) - 64 = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 + 8 x + 8 \cdot 8 - 64 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 + 8 x + 8 \cdot 8 - 64 = 0$

Move $8$ to the left of $x$ .

$x^{2} + 8 \cdot x + 8 x + 8 \cdot 8 - 64 = 0$

Multiply $8$ by $8$ .

$x^{2} + 8 x + 8 x + 64 - 64 = 0$

Add $8 x$ and $8 x$ .

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

Combine the opposite terms in $x^{2} + 16 x + 64 - 64$ .

Subtract $64$ from $64$ .

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

Add $x^{2} + 16 x$ and $0$ .

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

Step 3

Factor $x$ out of $x^{2} + 16 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x + 16 x = 0$

Factor $x$ out of $16 x$ .

$x \cdot x + x \cdot 16 = 0$

Factor $x$ out of $x \cdot x + x \cdot 16$ .

$x (x + 16) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 16 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x + 16$ equal to $0$ and solve for $x$ .

Set $x + 16$ equal to $0$ .

$x + 16 = 0$

Subtract $16$ from both sides of the equation.

$x = - 16$

Step 7

The final solution is all the values that make $x (x + 16) = 0$ true.

$x = 0, - 16$

Solve by Factoring (x+8)^2=64

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