Solve Using the Square Root Property (2x-1)^2=9

${(2 x - 1)}^{2} = 9$

Step 1

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

$2 x - 1 = \pm \sqrt{9}$

Step 2

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$2 x - 1 = \pm \sqrt{3^{2}}$

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

$2 x - 1 = \pm 3$

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.

$2 x - 1 = 3$

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

Add $1$ to both sides of the equation.

$2 x = 3 + 1$

Add $3$ and $1$ .

$2 x = 4$

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 $2$ .

$x = 2$

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

$2 x - 1 = - 3$

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

Add $1$ to both sides of the equation.

$2 x = - 3 + 1$

Add $- 3$ and $1$ .

$2 x = - 2$

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 $2$ .

$x = - 1$

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

$x = 2, - 1$

Solve Using the Square Root Property (2x-1)^2=9

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