Solve by Completing the Square x^2+8x=4

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

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.

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

Step 3

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 4

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

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

Step 5

Solve the equation for $x$ .

Take the square 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 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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