Solve by Completing the Square x^2-8x-5=0

$x^{2} - 8 x - 5 = 0$

Add $5$ to both sides of the equation.

$x^{2} - 8 x = 5$

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

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

Add the term to each side of the equation.

$x^{2} - 8 x + {(- 4)}^{2} = 5 + {(- 4)}^{2}$

Simplify the equation.

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

$x^{2} - 8 x + 16 = 5 + {(- 4)}^{2}$

Simplify $5 + {(- 4)}^{2}$ .

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

$x^{2} - 8 x + 16 = 5 + 16$

Add $5$ and $16$ .

$x^{2} - 8 x + 16 = 21$

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

${(x - 4)}^{2} = 21$

Solve the equation for $x$ .

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Take the square root of each side of the equation to set up the solution for $x$

${(x - 4)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{21}$

Remove the perfect root factor $x - 4$ under the radical to solve for $x$ .

$x - 4 = \pm \sqrt{21}$

Remove parentheses.

$x - 4 = \pm \sqrt{21}$

Add $4$ to both sides of the equation.

$x = \pm \sqrt{21} + 4$

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{21} + 4$

Decimal Form:

$x = 8.58257569 \dots, - 0.58257569 \dots$

Solve by Completing the Square x^2-8x-5=0

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