Solve by Factoring (4x-16)^(1/2)=36

${(4 x - 16)}^{\frac{1}{2}} = 36$

Step 1

Subtract $36$ from both sides of the equation.

${(4 x - 16)}^{\frac{1}{2}} - 36 = 0$

Step 2

Add $36$ to both sides of the equation.

${(4 x - 16)}^{\frac{1}{2}} = 36$

Step 3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${({(4 x - 16)}^{\frac{1}{2}})}^{2} = 36^{2}$

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${({(4 x - 16)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x - 16)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(4 x - 16)}^{\frac{1}{2} \cdot 2} = 36^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x - 16)}^{\frac{1}{2} \cdot 2} = 36^{2}$

Rewrite the expression.

${(4 x - 16)}^{1} = 36^{2}$

Simplify.

$4 x - 16 = 36^{2}$

Simplify the right side.

Raise $36$ to the power of $2$ .

$4 x - 16 = 1296$

Step 5

Solve for $x$ .

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

Add $16$ to both sides of the equation.

$4 x = 1296 + 16$

Add $1296$ and $16$ .

$4 x = 1312$

Divide each term in $4 x = 1312$ by $4$ and simplify.

Divide each term in $4 x = 1312$ by $4$ .

$\frac{4 x}{4} = \frac{1312}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{1312}{4}$

Divide $x$ by $1$ .

$x = \frac{1312}{4}$

Simplify the right side.

Divide $1312$ by $4$ .

$x = 328$

Solve by Factoring (4x-16)^(1/2)=36

Related Questions

Support LCMGCF.com by disabling your adblocker.