Solve for x 2(x-9)^2+13=21

$2 {(x - 9)}^{2} + 13 = 21$

Step 1

Subtract $13$ from both sides of the equation.

$2 {(x - 9)}^{2} = 21 - 13$

Step 2

Subtract $13$ from $21$ .

$2 {(x - 9)}^{2} = 8$

Step 3

Divide each term in $2 {(x - 9)}^{2} = 8$ by $2$ and simplify.

Divide each term in $2 {(x - 9)}^{2} = 8$ by $2$ .

$\frac{2 {(x - 9)}^{2}}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x - 9)}^{2}}{2} = \frac{8}{2}$

Divide ${(x - 9)}^{2}$ by $1$ .

${(x - 9)}^{2} = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

${(x - 9)}^{2} = 4$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 9 = \pm \sqrt{4}$

Step 5

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x - 9 = \pm \sqrt{2^{2}}$

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

$x - 9 = \pm 2$

Step 6

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.

$x - 9 = 2$

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

Add $9$ to both sides of the equation.

$x = 2 + 9$

Add $2$ and $9$ .

$x = 11$

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

$x - 9 = - 2$

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

Add $9$ to both sides of the equation.

$x = - 2 + 9$

Add $- 2$ and $9$ .

$x = 7$

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

$x = 11, 7$

Solve for x 2(x-9)^2+13=21

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