Write as a Set of Linear Factors (x-2)^(2/5)=9

${(x - 2)}^{\frac{2}{5}} = 9$

Step 1

Subtract $9$ from both sides of the equation.

${(x - 2)}^{\frac{2}{5}} - 9 = 0$

Step 2

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

${({(x - 2)}^{\frac{1}{5}})}^{2} - 9 = 0$

Step 3

Rewrite $9$ as $3^{2}$ .

${({(x - 2)}^{\frac{1}{5}})}^{2} - 3^{2} = 0$

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 $b = 3$ .

$({(x - 2)}^{\frac{1}{5}} + 3) ({(x - 2)}^{\frac{1}{5}} - 3) = 0$

Write as a Set of Linear Factors (x-2)^(2/5)=9

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