Solve for m square root of 5m+6+ square root of 3m+4=0

$\sqrt{5 m + 6} + \sqrt{3 m + 4} = 0$

Subtract $\sqrt{3 m + 4}$ from both sides of the equation.

$\sqrt{5 m + 6} = - \sqrt{3 m + 4}$

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

${\sqrt{5 m + 6}}^{2} = {(- \sqrt{3 m + 4})}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 m + 6}$ as ${(5 m + 6)}^{\frac{1}{2}}$ .

${({(5 m + 6)}^{\frac{1}{2}})}^{2} = {(- \sqrt{3 m + 4})}^{2}$

Simplify the left side.

Simplify ${({(5 m + 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 m + 6)}^{\frac{1}{2}})}^{2}$ .

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

${(5 m + 6)}^{\frac{1}{2} \cdot 2} = {(- \sqrt{3 m + 4})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 m + 6)}^{\frac{1}{2} \cdot 2} = {(- \sqrt{3 m + 4})}^{2}$

Rewrite the expression.

${(5 m + 6)}^{1} = {(- \sqrt{3 m + 4})}^{2}$

Simplify.

$5 m + 6 = {(- \sqrt{3 m + 4})}^{2}$

Simplify the right side.

Simplify ${(- \sqrt{3 m + 4})}^{2}$ .

Simplify the expression.

Apply the product rule to $- \sqrt{3 m + 4}$ .

$5 m + 6 = {(- 1)}^{2} {\sqrt{3 m + 4}}^{2}$

Raise $- 1$ to the power of $2$ .

$5 m + 6 = 1 {\sqrt{3 m + 4}}^{2}$

Multiply ${\sqrt{3 m + 4}}^{2}$ by $1$ .

$5 m + 6 = {\sqrt{3 m + 4}}^{2}$

Rewrite ${\sqrt{3 m + 4}}^{2}$ as $3 m + 4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 m + 4}$ as ${(3 m + 4)}^{\frac{1}{2}}$ .

$5 m + 6 = {({(3 m + 4)}^{\frac{1}{2}})}^{2}$

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

$5 m + 6 = {(3 m + 4)}^{\frac{1}{2} \cdot 2}$

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

$5 m + 6 = {(3 m + 4)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5 m + 6 = {(3 m + 4)}^{\frac{2}{2}}$

Rewrite the expression.

$5 m + 6 = {(3 m + 4)}^{1}$

Simplify.

$5 m + 6 = 3 m + 4$

Solve for $m$ .

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

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

$5 m + 6 - 3 m = 4$

Subtract $3 m$ from $5 m$ .

$2 m + 6 = 4$

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

Subtract $6$ from both sides of the equation.

$2 m = 4 - 6$

Subtract $6$ from $4$ .

$2 m = - 2$

Divide each term in $2 m = - 2$ by $2$ and simplify.

Divide each term in $2 m = - 2$ by $2$ .

$\frac{2 m}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{- 2}{2}$

Divide $m$ by $1$ .

$m = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$m = - 1$

Exclude the solutions that do not make $\sqrt{5 m + 6} + \sqrt{3 m + 4} = 0$ true.

$No solution$

Solve for m square root of 5m+6+ square root of 3m+4=0

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