Solve by Completing the Square 2x^2+20x=10

$2 x^{2} + 20 x = 10$

Step 1

Divide each term in $2 x^{2} + 20 x = 10$ by $2$ and simplify.

Divide each term in $2 x^{2} + 20 x = 10$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{20 x}{2} = \frac{10}{2}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{20 x}{2} = \frac{10}{2}$

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

$x^{2} + \frac{20 x}{2} = \frac{10}{2}$

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

Factor $2$ out of $20 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $10 x$ by $1$ .

$x^{2} + 10 x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x^{2} + 10 x = 5$

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.

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

Step 4

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

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

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

$x^{2} + 10 x + 25 = 5 + 25$

Add $5$ and $25$ .

$x^{2} + 10 x + 25 = 30$

Step 5

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

${(x + 5)}^{2} = 30$

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.

$x + 5 = \pm \sqrt{30}$

Subtract $5$ from both sides of the equation.

$x = \pm \sqrt{30} - 5$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{30} - 5$

Decimal Form:

$x = 0.47722557 \dots, - 10.47722557 \dots$

Solve by Completing the Square 2x^2+20x=10

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