Solve for m square root of 25-2m = square root of 10+3m

$\sqrt{25 - 2 m} = \sqrt{10 + 3 m}$

Step 1

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

${\sqrt{25 - 2 m}}^{2} = {\sqrt{10 + 3 m}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{25 - 2 m}$ as ${(25 - 2 m)}^{\frac{1}{2}}$ .

${({(25 - 2 m)}^{\frac{1}{2}})}^{2} = {\sqrt{10 + 3 m}}^{2}$

Simplify the left side.

Simplify ${({(25 - 2 m)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(25 - 2 m)}^{\frac{1}{2}})}^{2}$ .

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

${(25 - 2 m)}^{\frac{1}{2} \cdot 2} = {\sqrt{10 + 3 m}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(25 - 2 m)}^{\frac{1}{2} \cdot 2} = {\sqrt{10 + 3 m}}^{2}$

Rewrite the expression.

${(25 - 2 m)}^{1} = {\sqrt{10 + 3 m}}^{2}$

Simplify.

$25 - 2 m = {\sqrt{10 + 3 m}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{10 + 3 m}}^{2}$ as $10 + 3 m$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 + 3 m}$ as ${(10 + 3 m)}^{\frac{1}{2}}$ .

$25 - 2 m = {({(10 + 3 m)}^{\frac{1}{2}})}^{2}$

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

$25 - 2 m = {(10 + 3 m)}^{\frac{1}{2} \cdot 2}$

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

$25 - 2 m = {(10 + 3 m)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 - 2 m = {(10 + 3 m)}^{\frac{2}{2}}$

Rewrite the expression.

$25 - 2 m = {(10 + 3 m)}^{1}$

Simplify.

$25 - 2 m = 10 + 3 m$

Step 3

Solve for $m$ .

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

Subtract $3 m$ from both sides of the equation.

$25 - 2 m - 3 m = 10$

Subtract $3 m$ from $- 2 m$ .

$25 - 5 m = 10$

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

Subtract $25$ from both sides of the equation.

$- 5 m = 10 - 25$

Subtract $25$ from $10$ .

$- 5 m = - 15$

Divide each term in $- 5 m = - 15$ by $- 5$ and simplify.

Divide each term in $- 5 m = - 15$ by $- 5$ .

$\frac{- 5 m}{- 5} = \frac{- 15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 m}{- 5} = \frac{- 15}{- 5}$

Divide $m$ by $1$ .

$m = \frac{- 15}{- 5}$

Simplify the right side.

Divide $- 15$ by $- 5$ .

$m = 3$

Solve for m square root of 25-2m = square root of 10+3m

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