Solve for n. sqrt –3n = sqrt ( –4n − 1) n = _____

Square Both Sides: Square both sides of the equation to eliminate the square roots. (sqrt(–3n))^2 = (sqrt(–4n − 1))^2 –3n = –4n − 1Add N Terms: Add 4n to both sides to get all the n terms on one side. –3n + 4n = –4n + 4n − 1 n = −1Check Solution: Check the solution by substituting n back into the original equation to ensure both sides are equal. sqrt(–3(−1)) = sqrt(–4(−1) − 1) sqrt(3) = sqrt(4 − 1) sqrt(3) = sqrt(3)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $n$ . $\newline$ $\sqrt{\,-3n} = \sqrt{\,-4n - 1}$ $\newline$ $n = \,\_\_\_\_$

View step-by-step help

Home

Math Problems

Precalculus

Solve radical equations

Full solution

Q. Solve for

n

\newline

\sqrt{\,-3n} = \sqrt{\,-4n - 1}

\newline

n = \,\_\_\_\_

Square Both Sides: Square both sides of the equation to eliminate the square roots. $\newline$ $(\sqrt{-3n})^2 = (\sqrt{-4n - 1})^2$ $\newline$ $-3n = -4n - 1$
Add N Terms: Add $4n$ to both sides to get all the $n$ terms on one side. $\newline$ $-3n + 4n = -4n + 4n - 1$ $\newline$ $n = -1$
Check Solution: Check the solution by substituting $n$ back into the original equation to ensure both sides are equal. $\newline$ $\sqrt{(\text{–}3(\text{−}1))} = \sqrt{(\text{–}4(\text{−}1) \text{−} 1)}$ $\newline$ $\sqrt{3} = \sqrt{4 \text{−} 1}$ $\newline$ $\sqrt{3} = \sqrt{3}$