Solve for p square root of -10-2p = square root of 3p+40

$\sqrt{- 10 - 2 p} = \sqrt{3 p + 40}$

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

${\sqrt{- 10 - 2 p}}^{2} = {\sqrt{3 p + 40}}^{2}$

Simplify each side of the equation.

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

${({(- 10 - 2 p)}^{\frac{1}{2}})}^{2} = {\sqrt{3 p + 40}}^{2}$

Simplify the left side.

Simplify ${({(- 10 - 2 p)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(- 10 - 2 p)}^{\frac{1}{2}})}^{2}$ .

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

${(- 10 - 2 p)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 p + 40}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(- 10 - 2 p)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 p + 40}}^{2}$

Rewrite the expression.

${(- 10 - 2 p)}^{1} = {\sqrt{3 p + 40}}^{2}$

Simplify.

$- 10 - 2 p = {\sqrt{3 p + 40}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 p + 40}}^{2}$ as $3 p + 40$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 p + 40}$ as ${(3 p + 40)}^{\frac{1}{2}}$ .

$- 10 - 2 p = {({(3 p + 40)}^{\frac{1}{2}})}^{2}$

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

$- 10 - 2 p = {(3 p + 40)}^{\frac{1}{2} \cdot 2}$

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

$- 10 - 2 p = {(3 p + 40)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 10 - 2 p = {(3 p + 40)}^{\frac{2}{2}}$

Rewrite the expression.

$- 10 - 2 p = {(3 p + 40)}^{1}$

Simplify.

$- 10 - 2 p = 3 p + 40$

Solve for $p$ .

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

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

$- 10 - 2 p - 3 p = 40$

Subtract $3 p$ from $- 2 p$ .

$- 10 - 5 p = 40$

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

Add $10$ to both sides of the equation.

$- 5 p = 40 + 10$

Add $40$ and $10$ .

$- 5 p = 50$

Divide each term in $- 5 p = 50$ by $- 5$ and simplify.

Divide each term in $- 5 p = 50$ by $- 5$ .

$\frac{- 5 p}{- 5} = \frac{50}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 p}{- 5} = \frac{50}{- 5}$

Divide $p$ by $1$ .

$p = \frac{50}{- 5}$

Simplify the right side.

Divide $50$ by $- 5$ .

$p = - 10$

Solve for p square root of -10-2p = square root of 3p+40

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