Algebra Examples

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

Step 1

Subtract $4$ from both sides of the equation.

${(x - 2)}^{\frac{2}{5}} - 4 = 0$

Step 2

Rewrite ${(x - 2)}^{\frac{2}{5}}$ as ${({(x - 2)}^{\frac{1}{5}})}^{2}$ .

${({(x - 2)}^{\frac{1}{5}})}^{2} - 4 = 0$

Step 3

Rewrite $4$ as $2^{2}$ .

${({(x - 2)}^{\frac{1}{5}})}^{2} - 2^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = {(x - 2)}^{\frac{1}{5}}$ and $b = 2$ .

$({(x - 2)}^{\frac{1}{5}} + 2) ({(x - 2)}^{\frac{1}{5}} - 2) = 0$