Find All Complex Solutions cube root of x+2=5

$\sqrt[3]{x + 2} = 5$

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

${\sqrt[3]{x + 2}}^{3} = 5^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x + 2}$ as ${(x + 2)}^{\frac{1}{3}}$ .

${({(x + 2)}^{\frac{1}{3}})}^{3} = 5^{3}$

Simplify the left side.

Simplify ${({(x + 2)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x + 2)}^{\frac{1}{3}})}^{3}$ .

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

${(x + 2)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x + 2)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Rewrite the expression.

${(x + 2)}^{1} = 5^{3}$

Simplify.

$x + 2 = 5^{3}$

Simplify the right side.

Raise $5$ to the power of $3$ .

$x + 2 = 125$

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

Subtract $2$ from both sides of the equation.

$x = 125 - 2$

Subtract $2$ from $125$ .

$x = 123$