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

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

Step 1

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

$5 x - 2 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

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

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

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

$5 x - 2 = \pm 5$

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.

$5 x - 2 = 5$

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

Add $2$ to both sides of the equation.

$5 x = 5 + 2$

Add $5$ and $2$ .

$5 x = 7$

Divide each term in $5 x = 7$ by $5$ and simplify.

Divide each term in $5 x = 7$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5}$

Divide $x$ by $1$ .

$x = \frac{7}{5}$

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

$5 x - 2 = - 5$

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

Add $2$ to both sides of the equation.

$5 x = - 5 + 2$

Add $- 5$ and $2$ .

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

$\frac{5 x}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 3}{5}$

Divide $x$ by $1$ .

$x = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{5}$

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

$x = \frac{7}{5}, - \frac{3}{5}$

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

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