Solve for x 3(x-3)^2+2=26

$3 {(x - 3)}^{2} + 2 = 26$

Step 1

Subtract $2$ from both sides of the equation.

$3 {(x - 3)}^{2} = 26 - 2$

Step 2

Subtract $2$ from $26$ .

$3 {(x - 3)}^{2} = 24$

Step 3

Divide each term in $3 {(x - 3)}^{2} = 24$ by $3$ and simplify.

Divide each term in $3 {(x - 3)}^{2} = 24$ by $3$ .

$\frac{3 {(x - 3)}^{2}}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(x - 3)}^{2}}{3} = \frac{24}{3}$

Divide ${(x - 3)}^{2}$ by $1$ .

${(x - 3)}^{2} = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

${(x - 3)}^{2} = 8$

Step 4

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

$x - 3 = \pm \sqrt{8}$

Step 5

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x - 3 = \pm \sqrt{4 (2)}$

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

$x - 3 = \pm \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$x - 3 = \pm 2 \sqrt{2}$

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.

$x - 3 = 2 \sqrt{2}$

Add $3$ to both sides of the equation.

$x = 2 \sqrt{2} + 3$

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

$x - 3 = - 2 \sqrt{2}$

Add $3$ to both sides of the equation.

$x = - 2 \sqrt{2} + 3$

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

$x = 2 \sqrt{2} + 3, - 2 \sqrt{2} + 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{2} + 3, - 2 \sqrt{2} + 3$

Decimal Form:

$x = 5.82842712 \dots, 0.17157287 \dots$

Solve for x 3(x-3)^2+2=26

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