Solve Using the Square Root Property (9x-4)^2=36

${(9 x - 4)}^{2} = 36$

Step 1

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

$9 x - 4 = \pm \sqrt{36}$

Step 2

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$9 x - 4 = \pm \sqrt{6^{2}}$

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

$9 x - 4 = \pm 6$

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.

$9 x - 4 = 6$

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

Add $4$ to both sides of the equation.

$9 x = 6 + 4$

Add $6$ and $4$ .

$9 x = 10$

Divide each term in $9 x = 10$ by $9$ and simplify.

Divide each term in $9 x = 10$ by $9$ .

$\frac{9 x}{9} = \frac{10}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{10}{9}$

Divide $x$ by $1$ .

$x = \frac{10}{9}$

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

$9 x - 4 = - 6$

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

Add $4$ to both sides of the equation.

$9 x = - 6 + 4$

Add $- 6$ and $4$ .

$9 x = - 2$

Divide each term in $9 x = - 2$ by $9$ and simplify.

Divide each term in $9 x = - 2$ by $9$ .

$\frac{9 x}{9} = \frac{- 2}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 2}{9}$

Divide $x$ by $1$ .

$x = \frac{- 2}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{9}$

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

$x = \frac{10}{9}, - \frac{2}{9}$

Solve Using the Square Root Property (9x-4)^2=36

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