Solve Using the Square Root Property (5x+1)^2=25

${(5 x + 1)}^{2} = 25$

Step 1

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

$5 x + 1 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

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

$5 x + 1 = \pm \sqrt{5^{2}}$

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

$5 x + 1 = \pm 5$

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.

$5 x + 1 = 5$

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

Subtract $1$ from both sides of the equation.

$5 x = 5 - 1$

Subtract $1$ from $5$ .

$5 x = 4$

Divide each term in $5 x = 4$ by $5$ and simplify.

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Divide $x$ by $1$ .

$x = \frac{4}{5}$

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

$5 x + 1 = - 5$

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

Subtract $1$ from both sides of the equation.

$5 x = - 5 - 1$

Subtract $1$ from $- 5$ .

$5 x = - 6$

Divide each term in $5 x = - 6$ by $5$ and simplify.

Divide each term in $5 x = - 6$ by $5$ .

$\frac{5 x}{5} = \frac{- 6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 6}{5}$

Divide $x$ by $1$ .

$x = \frac{- 6}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{6}{5}$

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

$x = \frac{4}{5}, - \frac{6}{5}$

Solve Using the Square Root Property (5x+1)^2=25

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