Solve by Completing the Square 2x^2+12x=32

$2 x^{2} + 12 x = 32$

Step 1

Divide each term in $2 x^{2} + 12 x = 32$ by $2$ and simplify.

Divide each term in $2 x^{2} + 12 x = 32$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{12 x}{2} = \frac{32}{2}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{12 x}{2} = \frac{32}{2}$

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

$x^{2} + \frac{12 x}{2} = \frac{32}{2}$

Cancel the common factor of $12$ and $2$ .

Factor $2$ out of $12 x$ .

$x^{2} + \frac{2 (6 x)}{2} = \frac{32}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x^{2} + \frac{2 (6 x)}{2 (1)} = \frac{32}{2}$

Cancel the common factor.

$x^{2} + \frac{2 (6 x)}{2 \cdot 1} = \frac{32}{2}$

Rewrite the expression.

$x^{2} + \frac{6 x}{1} = \frac{32}{2}$

Divide $6 x$ by $1$ .

$x^{2} + 6 x = \frac{32}{2}$

Simplify the right side.

Divide $32$ by $2$ .

$x^{2} + 6 x = 16$

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 $b$ .

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = 16 + {(3)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 16 + {(3)}^{2}$

Simplify the right side.

Simplify $16 + {(3)}^{2}$ .

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 16 + 9$

Add $16$ and $9$ .

$x^{2} + 6 x + 9 = 25$

Step 5

Factor the perfect trinomial square into ${(x + 3)}^{2}$ .

${(x + 3)}^{2} = 25$

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.

$x + 3 = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x + 3 = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x + 3 = \pm 5$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x + 3 = 5$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$x = 5 - 3$

Subtract $3$ from $5$ .

$x = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$x + 3 = - 5$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$x = - 5 - 3$

Subtract $3$ from $- 5$ .

$x = - 8$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 8$

Solve by Completing the Square 2x^2+12x=32

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