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

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

Step 1

Rewrite the equation as $\sqrt{10 + 3 m} = \sqrt{25 - 25}$ .

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

Simplify ${({(10 + 3 m)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(10 + 3 m)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${\sqrt{25 - 25}}^{2}$ .

Subtract $25$ from $25$ .

$10 + 3 m = {\sqrt{0}}^{2}$

Rewrite $0$ as $0^{2}$ .

$10 + 3 m = {\sqrt{0^{2}}}^{2}$

Pull terms out from under the radical, assuming positive real numbers.

$10 + 3 m = 0^{2}$

Raising $0$ to any positive power yields $0$ .

$10 + 3 m = 0$

Step 4

Solve for $m$ .

Subtract $10$ from both sides of the equation.

$3 m = - 10$

Divide each term in $3 m = - 10$ by $3$ and simplify.

Divide each term in $3 m = - 10$ by $3$ .

$\frac{3 m}{3} = \frac{- 10}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} = \frac{- 10}{3}$

Divide $m$ by $1$ .

$m = \frac{- 10}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$m = - \frac{10}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{10}{3}$

Decimal Form:

$m = - 3.\overline{3}$

Mixed Number Form:

$m = - 3 \frac{1}{3}$

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

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