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

${(2 x - 5)}^{2} = 81$

Step 1

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

$2 x - 5 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

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

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

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

$2 x - 5 = \pm 9$

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.

$2 x - 5 = 9$

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

Add $5$ to both sides of the equation.

$2 x = 9 + 5$

Add $9$ and $5$ .

$2 x = 14$

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$

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

$2 x - 5 = - 9$

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

Add $5$ to both sides of the equation.

$2 x = - 9 + 5$

Add $- 9$ and $5$ .

$2 x = - 4$

Divide each term in $2 x = - 4$ by $2$ and simplify.

Divide each term in $2 x = - 4$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

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

$x = 7, - 2$

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

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