Solve for x (3x+8)^2-12=37

${(3 x + 8)}^{2} - 12 = 37$

Step 1

Add $12$ to both sides of the equation.

${(3 x + 8)}^{2} = 37 + 12$

Step 2

Add $37$ and $12$ .

${(3 x + 8)}^{2} = 49$

Step 3

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

$3 x + 8 = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$3 x + 8 = \pm \sqrt{7^{2}}$

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

$3 x + 8 = \pm 7$

Step 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.

$3 x + 8 = 7$

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

Subtract $8$ from both sides of the equation.

$3 x = 7 - 8$

Subtract $8$ from $7$ .

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

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

$3 x + 8 = - 7$

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

Subtract $8$ from both sides of the equation.

$3 x = - 7 - 8$

Subtract $8$ from $- 7$ .

$3 x = - 15$

Divide each term in $3 x = - 15$ by $3$ and simplify.

Divide each term in $3 x = - 15$ by $3$ .

$\frac{3 x}{3} = \frac{- 15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 15}{3}$

Divide $x$ by $1$ .

$x = \frac{- 15}{3}$

Simplify the right side.

Divide $- 15$ by $3$ .

$x = - 5$

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

$x = - \frac{1}{3}, - 5$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{3}, - 5$

Decimal Form:

$x = - 0.\overline{3}, - 5$

Solve for x (3x+8)^2-12=37

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