Solve Using the Square Root Property (5x+8)^2=81

${(5 x + 8)}^{2} = 81$

Step 1

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

$5 x + 8 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

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

$5 x + 8 = \pm \sqrt{9^{2}}$

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

$5 x + 8 = \pm 9$

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.

$5 x + 8 = 9$

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

Subtract $8$ from both sides of the equation.

$5 x = 9 - 8$

Subtract $8$ from $9$ .

$5 x = 1$

Divide each term in $5 x = 1$ by $5$ and simplify.

Divide each term in $5 x = 1$ by $5$ .

$\frac{5 x}{5} = \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{1}{5}$

Divide $x$ by $1$ .

$x = \frac{1}{5}$

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

$5 x + 8 = - 9$

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

Subtract $8$ from both sides of the equation.

$5 x = - 9 - 8$

Subtract $8$ from $- 9$ .

$5 x = - 17$

Divide each term in $5 x = - 17$ by $5$ and simplify.

Divide each term in $5 x = - 17$ by $5$ .

$\frac{5 x}{5} = \frac{- 17}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 17}{5}$

Divide $x$ by $1$ .

$x = \frac{- 17}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{17}{5}$

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

$x = \frac{1}{5}, - \frac{17}{5}$

Solve Using the Square Root Property (5x+8)^2=81

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