Solve for c -36=-9(c-12)^(1/2)

$- 36 = - 9 {(c - 12)}^{\frac{1}{2}}$

Step 1

Rewrite the equation as $- 9 {(c - 12)}^{\frac{1}{2}} = - 36$ .

$- 9 {(c - 12)}^{\frac{1}{2}} = - 36$

Step 2

Divide each term in $- 9 {(c - 12)}^{\frac{1}{2}} = - 36$ by $- 9$ and simplify.

Divide each term in $- 9 {(c - 12)}^{\frac{1}{2}} = - 36$ by $- 9$ .

$\frac{- 9 {(c - 12)}^{\frac{1}{2}}}{- 9} = \frac{- 36}{- 9}$

Simplify the left side.

Cancel the common factor.

$\frac{- 9 {(c - 12)}^{\frac{1}{2}}}{- 9} = \frac{- 36}{- 9}$

Divide ${(c - 12)}^{\frac{1}{2}}$ by $1$ .

${(c - 12)}^{\frac{1}{2}} = \frac{- 36}{- 9}$

Simplify the right side.

Divide $- 36$ by $- 9$ .

${(c - 12)}^{\frac{1}{2}} = 4$

Step 3

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

${({(c - 12)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${({(c - 12)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(c - 12)}^{\frac{1}{2}})}^{2}$ .

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

${(c - 12)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(c - 12)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(c - 12)}^{1} = 4^{2}$

Simplify.

$c - 12 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$c - 12 = 16$

Step 5

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

Add $12$ to both sides of the equation.

$c = 16 + 12$

Add $16$ and $12$ .

$c = 28$