Solve Using the Square Root Property (9x-5)^2=25

${(9 x - 5)}^{2} = 25$

Step 1

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

$9 x - 5 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

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

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

$9 x - 5 = \pm 5$

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.

$9 x - 5 = 5$

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

Add $5$ to both sides of the equation.

$9 x = 5 + 5$

Add $5$ and $5$ .

$9 x = 10$

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.

$9 x - 5 = - 5$

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

Add $5$ to both sides of the equation.

$9 x = - 5 + 5$

Add $- 5$ and $5$ .

$9 x = 0$

Divide each term in $9 x = 0$ by $9$ and simplify.

Divide each term in $9 x = 0$ by $9$ .

$\frac{9 x}{9} = \frac{0}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{0}{9}$

Divide $x$ by $1$ .

$x = \frac{0}{9}$

Simplify the right side.

Divide $0$ by $9$ .

$x = 0$

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

$x = \frac{10}{9}, 0$

Solve Using the Square Root Property (9x-5)^2=25

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