Solve Using the Square Root Property (2x+7)^2=81

${(2 x + 7)}^{2} = 81$

Step 1

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

$2 x + 7 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$2 x + 7 = \pm \sqrt{9^{2}}$

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

$2 x + 7 = \pm 9$

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.

$2 x + 7 = 9$

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

Subtract $7$ from both sides of the equation.

$2 x = 9 - 7$

Subtract $7$ from $9$ .

$2 x = 2$

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

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

$2 x + 7 = - 9$

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

Subtract $7$ from both sides of the equation.

$2 x = - 9 - 7$

Subtract $7$ from $- 9$ .

$2 x = - 16$

Divide each term in $2 x = - 16$ by $2$ and simplify.

Divide each term in $2 x = - 16$ by $2$ .

$\frac{2 x}{2} = \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 16}{2}$

Divide $x$ by $1$ .

$x = \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$x = - 8$

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

$x = 1, - 8$

Solve Using the Square Root Property (2x+7)^2=81

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