Solve Using the Square Root Property (7x-3)^2=25

${(7 x - 3)}^{2} = 25$

Step 1

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

$7 x - 3 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

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

$7 x - 3 = \pm \sqrt{5^{2}}$

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

$7 x - 3 = \pm 5$

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.

$7 x - 3 = 5$

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

Add $3$ to both sides of the equation.

$7 x = 5 + 3$

Add $5$ and $3$ .

$7 x = 8$

Divide each term in $7 x = 8$ by $7$ and simplify.

Divide each term in $7 x = 8$ by $7$ .

$\frac{7 x}{7} = \frac{8}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{8}{7}$

Divide $x$ by $1$ .

$x = \frac{8}{7}$

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

$7 x - 3 = - 5$

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

Add $3$ to both sides of the equation.

$7 x = - 5 + 3$

Add $- 5$ and $3$ .

$7 x = - 2$

Divide each term in $7 x = - 2$ by $7$ and simplify.

Divide each term in $7 x = - 2$ by $7$ .

$\frac{7 x}{7} = \frac{- 2}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 2}{7}$

Divide $x$ by $1$ .

$x = \frac{- 2}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{7}$

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

$x = \frac{8}{7}, - \frac{2}{7}$

Solve Using the Square Root Property (7x-3)^2=25

Related Questions

Support LCMGCF.com by disabling your adblocker.