Find All Complex Solutions square root of x+72=5

$\sqrt{x + 72} = 5$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x + 72}}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 72}$ as ${(x + 72)}^{\frac{1}{2}}$ .

${({(x + 72)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(x + 72)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 72)}^{\frac{1}{2}})}^{2}$ .

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

${(x + 72)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 72)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(x + 72)}^{1} = 5^{2}$

Simplify.

$x + 72 = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$x + 72 = 25$

Step 3

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

Subtract $72$ from both sides of the equation.

$x = 25 - 72$

Subtract $72$ from $25$ .

$x = - 47$