Solve for m square root of 18-2m = square root of 2m-10

$\sqrt{18 - 2 m} = \sqrt{2 m - 10}$

Step 1

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

${\sqrt{18 - 2 m}}^{2} = {\sqrt{2 m - 10}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{18 - 2 m}$ as ${(18 - 2 m)}^{\frac{1}{2}}$ .

${({(18 - 2 m)}^{\frac{1}{2}})}^{2} = {\sqrt{2 m - 10}}^{2}$

Simplify the left side.

Simplify ${({(18 - 2 m)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(18 - 2 m)}^{\frac{1}{2}})}^{2}$ .

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

${(18 - 2 m)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 m - 10}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(18 - 2 m)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 m - 10}}^{2}$

Rewrite the expression.

${(18 - 2 m)}^{1} = {\sqrt{2 m - 10}}^{2}$

Simplify.

$18 - 2 m = {\sqrt{2 m - 10}}^{2}$

Simplify the right side.

Simplify ${\sqrt{2 m - 10}}^{2}$ .

Factor $2$ out of $2 m - 10$ .

Factor $2$ out of $2 m$ .

$18 - 2 m = {\sqrt{2 (m) - 10}}^{2}$

Factor $2$ out of $- 10$ .

$18 - 2 m = {\sqrt{2 m + 2 \cdot - 5}}^{2}$

Factor $2$ out of $2 m + 2 \cdot - 5$ .

$18 - 2 m = {\sqrt{2 (m - 5)}}^{2}$

Rewrite ${\sqrt{2 (m - 5)}}^{2}$ as $2 (m - 5)$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 (m - 5)}$ as ${(2 (m - 5))}^{\frac{1}{2}}$ .

$18 - 2 m = {({(2 (m - 5))}^{\frac{1}{2}})}^{2}$

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

$18 - 2 m = {(2 (m - 5))}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$18 - 2 m = {(2 (m - 5))}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$18 - 2 m = {(2 (m - 5))}^{\frac{2}{2}}$

Rewrite the expression.

$18 - 2 m = {(2 (m - 5))}^{1}$

Simplify.

$18 - 2 m = 2 (m - 5)$

Apply the distributive property.

$18 - 2 m = 2 m + 2 \cdot - 5$

Multiply $2$ by $- 5$ .

$18 - 2 m = 2 m - 10$

Step 3

Solve for $m$ .

Move all terms containing $m$ to the left side of the equation.

Subtract $2 m$ from both sides of the equation.

$18 - 2 m - 2 m = - 10$

Subtract $2 m$ from $- 2 m$ .

$18 - 4 m = - 10$

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

Subtract $18$ from both sides of the equation.

$- 4 m = - 10 - 18$

Subtract $18$ from $- 10$ .

$- 4 m = - 28$

Divide each term in $- 4 m = - 28$ by $- 4$ and simplify.

Divide each term in $- 4 m = - 28$ by $- 4$ .

$\frac{- 4 m}{- 4} = \frac{- 28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 m}{- 4} = \frac{- 28}{- 4}$

Divide $m$ by $1$ .

$m = \frac{- 28}{- 4}$

Simplify the right side.

Divide $- 28$ by $- 4$ .

$m = 7$

Solve for m square root of 18-2m = square root of 2m-10

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