Precalculus Examples

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

Step 1

Add $8$ to both sides of the equation.

$x^{2} - 8 x = 8$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 4)}^{2}$

Step 3

Add the term to each side of the equation.

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

Step 4

Simplify the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

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

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

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $8 + {(- 4)}^{2}$ .

Tap for more steps...

Step 4.2.1.1

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

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

Step 4.2.1.2

Add $8$ and $16$ .

$x^{2} - 8 x + 16 = 24$

Step 5

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

${(x - 4)}^{2} = 24$

Step 6

Solve the equation for $x$ .

Tap for more steps...

Step 6.1

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

$x - 4 = \pm \sqrt{24}$

Step 6.2

Simplify $\pm \sqrt{24}$ .

Tap for more steps...

Step 6.2.1

Rewrite $24$ as $2^{2} \cdot 6$ .

Tap for more steps...

Step 6.2.1.1

Factor $4$ out of $24$ .

$x - 4 = \pm \sqrt{4 (6)}$

Step 6.2.1.2

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

$x - 4 = \pm \sqrt{2^{2} \cdot 6}$

Step 6.2.2

Pull terms out from under the radical.

$x - 4 = \pm 2 \sqrt{6}$

Step 6.3

Add $4$ to both sides of the equation.

$x = \pm 2 \sqrt{6} + 4$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{6} + 4$

Decimal Form:

$x = 8.89897948 \dots, - 0.89897948 \dots$