Solve by Completing the Square 2x^2-20x=8

$2 x^{2} - 20 x = 8$

Step 1

Divide each term in $2 x^{2} - 20 x = 8$ by $2$ and simplify.

Divide each term in $2 x^{2} - 20 x = 8$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{- 20 x}{2} = \frac{8}{2}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{- 20 x}{2} = \frac{8}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{- 20 x}{2} = \frac{8}{2}$

Cancel the common factor of $- 20$ and $2$ .

Factor $2$ out of $- 20 x$ .

$x^{2} + \frac{2 (- 10 x)}{2} = \frac{8}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x^{2} + \frac{2 (- 10 x)}{2 (1)} = \frac{8}{2}$

Cancel the common factor.

$x^{2} + \frac{2 (- 10 x)}{2 \cdot 1} = \frac{8}{2}$

Rewrite the expression.

$x^{2} + \frac{- 10 x}{1} = \frac{8}{2}$

Divide $- 10 x$ by $1$ .

$x^{2} - 10 x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

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

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 $b$ .

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

Step 3

Add the term to each side of the equation.

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

Step 4

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

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

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

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

Add $4$ and $25$ .

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

Step 5

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

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

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.

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

Add $5$ to both sides of the equation.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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

Solve by Completing the Square 2x^2-20x=8

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