Solve by Completing the Square x^2-8x-10=18

$x^{2} - 8 x - 10 = 18$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $10$ to both sides of the equation.

$x^{2} - 8 x = 18 + 10$

Add $18$ and $10$ .

$x^{2} - 8 x = 28$

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.

$x^{2} - 8 x + {(- 4)}^{2} = 28 + {(- 4)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} - 8 x + 16 = 28 + {(- 4)}^{2}$

Simplify the right side.

Simplify $28 + {(- 4)}^{2}$ .

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

$x^{2} - 8 x + 16 = 28 + 16$

Add $28$ and $16$ .

$x^{2} - 8 x + 16 = 44$

Step 5

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

${(x - 4)}^{2} = 44$

Step 6

Solve the equation for $x$ .

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

$x - 4 = \pm \sqrt{44}$

Simplify $\pm \sqrt{44}$ .

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$x - 4 = \pm \sqrt{4 (11)}$

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

$x - 4 = \pm \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$x - 4 = \pm 2 \sqrt{11}$

Add $4$ to both sides of the equation.

$x = \pm 2 \sqrt{11} + 4$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{11} + 4$

Decimal Form:

$x = 10.63324958 \dots, - 2.63324958 \dots$

Solve by Completing the Square x^2-8x-10=18

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