Solve by Completing the Square 2x^2-8x=22

$2 x^{2} - 8 x = 22$

Step 1

Divide each term in $2 x^{2} - 8 x = 22$ by $2$ and simplify.

Divide each term in $2 x^{2} - 8 x = 22$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{- 8 x}{2} = \frac{22}{2}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{- 8 x}{2} = \frac{22}{2}$

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

$x^{2} + \frac{- 8 x}{2} = \frac{22}{2}$

Cancel the common factor of $- 8$ and $2$ .

Factor $2$ out of $- 8 x$ .

$x^{2} + \frac{2 (- 4 x)}{2} = \frac{22}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x^{2} + \frac{2 (- 4 x)}{2 (1)} = \frac{22}{2}$

Cancel the common factor.

$x^{2} + \frac{2 (- 4 x)}{2 \cdot 1} = \frac{22}{2}$

Rewrite the expression.

$x^{2} + \frac{- 4 x}{1} = \frac{22}{2}$

Divide $- 4 x$ by $1$ .

$x^{2} - 4 x = \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

$x^{2} - 4 x = 11$

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 $b$ .

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

Step 3

Add the term to each side of the equation.

$x^{2} - 4 x + {(- 2)}^{2} = 11 + {(- 2)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} - 4 x + 4 = 11 + {(- 2)}^{2}$

Simplify the right side.

Simplify $11 + {(- 2)}^{2}$ .

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

$x^{2} - 4 x + 4 = 11 + 4$

Add $11$ and $4$ .

$x^{2} - 4 x + 4 = 15$

Step 5

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

${(x - 2)}^{2} = 15$

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.

$x - 2 = \pm \sqrt{15}$

Add $2$ to both sides of the equation.

$x = \pm \sqrt{15} + 2$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{15} + 2$

Decimal Form:

$x = 5.87298334 \dots, - 1.87298334 \dots$

Solve by Completing the Square 2x^2-8x=22

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