Solve for a. sqrt ( –9 + 7a) = sqrt 6a a = _____

Square Both Sides: Square both sides of the equation to eliminate the square roots. (sqrt(–9 + 7a))^2 = (sqrt(6a))^2 –9 + 7a = 6aSubtract to Isolate 'a': Subtract 6a from both sides to get all the terms with 'a' on one side. 7a - 6a = 9 a = 9Check Solution: Check the solution by substituting 'a' back into the original equation to ensure both sides are equal. sqrt(–9 + 7*9) = sqrt(6*9) sqrt(–9 + 63) = sqrt(54) sqrt(54) = sqrt(54) Both sides are equal, so the solution is correct.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $a$ . $\newline$ $\sqrt{\,-9 + 7a} = \sqrt{\,6a}$ $\newline$ $a = \,\_\_\_\_\_$

View step-by-step help

Home

Math Problems

Precalculus

Solve radical equations

Full solution

Q. Solve for

a

\newline

\sqrt{\,-9 + 7a} = \sqrt{\,6a}

\newline

a = \,\_\_\_\_\_

Square Both Sides: Square both sides of the equation to eliminate the square roots. $\newline$ $(\sqrt{-9 + 7a})^2 = (\sqrt{6a})^2$ $\newline$ $-9 + 7a = 6a$
Subtract to Isolate 'a': Subtract $6a$ from both sides to get all the terms with 'a' on one side. $\newline$ $7a - 6a = 9$ $\newline$ $a = 9$
Check Solution: Check the solution by substituting $a$ back into the original equation to ensure both sides are equal. $\sqrt{(–9 + 7\times9)} = \sqrt{(6\times9)}$ $\sqrt{(–9 + 63)} = \sqrt{(54)}$ $\sqrt{(54)} = \sqrt{(54)}$ Both sides are equal, so the solution is correct.