Solve for n square root of -1-n = square root of 2n+17

$\sqrt{- 1 - n} = \sqrt{2 n + 17}$

Step 1

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

${\sqrt{- 1 - n}}^{2} = {\sqrt{2 n + 17}}^{2}$

Step 2

Simplify each side of the equation.

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

${({(- 1 - n)}^{\frac{1}{2}})}^{2} = {\sqrt{2 n + 17}}^{2}$

Simplify the left side.

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

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

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

${(- 1 - n)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 n + 17}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(- 1 - n)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 n + 17}}^{2}$

Rewrite the expression.

${(- 1 - n)}^{1} = {\sqrt{2 n + 17}}^{2}$

Simplify.

$- 1 - n = {\sqrt{2 n + 17}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{2 n + 17}}^{2}$ as $2 n + 17$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 n + 17}$ as ${(2 n + 17)}^{\frac{1}{2}}$ .

$- 1 - n = {({(2 n + 17)}^{\frac{1}{2}})}^{2}$

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

$- 1 - n = {(2 n + 17)}^{\frac{1}{2} \cdot 2}$

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

$- 1 - n = {(2 n + 17)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 - n = {(2 n + 17)}^{\frac{2}{2}}$

Rewrite the expression.

$- 1 - n = {(2 n + 17)}^{1}$

Simplify.

$- 1 - n = 2 n + 17$

Step 3

Solve for $n$ .

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

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

$- 1 - n - 2 n = 17$

Subtract $2 n$ from $- n$ .

$- 1 - 3 n = 17$

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

Add $1$ to both sides of the equation.

$- 3 n = 17 + 1$

Add $17$ and $1$ .

$- 3 n = 18$

Divide each term in $- 3 n = 18$ by $- 3$ and simplify.

Divide each term in $- 3 n = 18$ by $- 3$ .

$\frac{- 3 n}{- 3} = \frac{18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 n}{- 3} = \frac{18}{- 3}$

Divide $n$ by $1$ .

$n = \frac{18}{- 3}$

Simplify the right side.

Divide $18$ by $- 3$ .

$n = - 6$

Solve for n square root of -1-n = square root of 2n+17

Related Questions

Support LCMGCF.com by disabling your adblocker.