Solve Using the Square Root Property (3x+2)^2=100

${(3 x + 2)}^{2} = 100$

Step 1

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

$3 x + 2 = \pm \sqrt{100}$

Step 2

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

$3 x + 2 = \pm \sqrt{10^{2}}$

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

$3 x + 2 = \pm 10$

Step 3

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.

$3 x + 2 = 10$

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

Subtract $2$ from both sides of the equation.

$3 x = 10 - 2$

Subtract $2$ from $10$ .

$3 x = 8$

Divide each term in $3 x = 8$ by $3$ and simplify.

Divide each term in $3 x = 8$ by $3$ .

$\frac{3 x}{3} = \frac{8}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{8}{3}$

Divide $x$ by $1$ .

$x = \frac{8}{3}$

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

$3 x + 2 = - 10$

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

Subtract $2$ from both sides of the equation.

$3 x = - 10 - 2$

Subtract $2$ from $- 10$ .

$3 x = - 12$

Divide each term in $3 x = - 12$ by $3$ and simplify.

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x = - 4$

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

$x = \frac{8}{3}, - 4$

Solve Using the Square Root Property (3x+2)^2=100

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