Solve Using the Square Root Property (4x-5)^2=64

${(4 x - 5)}^{2} = 64$

Step 1

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

$4 x - 5 = \pm \sqrt{64}$

Step 2

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$4 x - 5 = \pm \sqrt{8^{2}}$

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

$4 x - 5 = \pm 8$

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.

$4 x - 5 = 8$

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

Add $5$ to both sides of the equation.

$4 x = 8 + 5$

Add $8$ and $5$ .

$4 x = 13$

Divide each term in $4 x = 13$ by $4$ and simplify.

Divide each term in $4 x = 13$ by $4$ .

$\frac{4 x}{4} = \frac{13}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{13}{4}$

Divide $x$ by $1$ .

$x = \frac{13}{4}$

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

$4 x - 5 = - 8$

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

Add $5$ to both sides of the equation.

$4 x = - 8 + 5$

Add $- 8$ and $5$ .

$4 x = - 3$

Divide each term in $4 x = - 3$ by $4$ and simplify.

Divide each term in $4 x = - 3$ by $4$ .

$\frac{4 x}{4} = \frac{- 3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3}{4}$

Divide $x$ by $1$ .

$x = \frac{- 3}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

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

$x = \frac{13}{4}, - \frac{3}{4}$

Solve Using the Square Root Property (4x-5)^2=64

Related Questions

Support LCMGCF.com by disabling your adblocker.