Solve Using the Square Root Property (2x-3)^2=81

${(2 x - 3)}^{2} = 81$

Step 1

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

$2 x - 3 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

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

$2 x - 3 = \pm \sqrt{9^{2}}$

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

$2 x - 3 = \pm 9$

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.

$2 x - 3 = 9$

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

Add $3$ to both sides of the equation.

$2 x = 9 + 3$

Add $9$ and $3$ .

$2 x = 12$

Divide each term in $2 x = 12$ by $2$ and simplify.

Divide each term in $2 x = 12$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2}$

Divide $x$ by $1$ .

$x = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$x = 6$

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

$2 x - 3 = - 9$

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

Add $3$ to both sides of the equation.

$2 x = - 9 + 3$

Add $- 9$ and $3$ .

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

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

$x = 6, - 3$

Solve Using the Square Root Property (2x-3)^2=81

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