Solve by Completing the Square x^2-10x-4=0

$x^{2} - 10 x - 4 = 0$

Add $4$ to both sides of the equation.

$x^{2} - 10 x = 4$

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

${(\frac{b}{2})}^{2} = {(- 5)}^{2}$

Add the term to each side of the equation.

$x^{2} - 10 x + {(- 5)}^{2} = 4 + {(- 5)}^{2}$

Simplify the equation.

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Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25 = 4 + {(- 5)}^{2}$

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

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Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25 = 4 + 25$

Add $4$ and $25$ .

$x^{2} - 10 x + 25 = 29$

Factor the perfect trinomial square into ${(x - 5)}^{2}$ .

${(x - 5)}^{2} = 29$

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 $x$

${(x - 5)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{29}$

Remove the perfect root factor $x - 5$ under the radical to solve for $x$ .

$x - 5 = \pm \sqrt{29}$

Remove parentheses.

$x - 5 = \pm \sqrt{29}$

Add $5$ to both sides of the equation.

$x = \pm \sqrt{29} + 5$

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{29} + 5$

Decimal Form:

$x = 10.38516480 \dots, - 0.38516480 \dots$

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