Solve for the specified variable. Assume that all other variables are nonzero
-$$81 \left( a ^ { 2 } - b \right) + 11 = 7 F ; \text { for } a$$
A) $a = \pm \frac { \sqrt { 7 \mathrm {~F} + 81 \mathrm {~b} - 11 } } { 9 }$
B) $a = \pm \frac { \sqrt { 7 F - 11 } } { 9 } + b$
C)$ a = \pm \frac { \sqrt { 7 F + b - 11 } } { 9 }$
D) $a = \pm \frac { \sqrt { 7 F - b + 11 } } { 9 }$

Question

Quizplus · Accepted Answer

First, isolate $a^2$ by subtracting 11 from both sides and then dividing by 81: $a^2 - b = \frac{7F - 11}{81}$. Then, add $b$ to both sides: $a^2 = \frac{7F - 11}{81} + b$. To solve for $a$, take the square root of both sides, leading to $a = \pm \sqrt{\frac{7F - 11}{81} + b}$. Simplifying inside the square root gives $a = \pm \frac{\sqrt{7F + 81b - 11}}{9}$, matching option A.

Solve for the Specified Variable 81(a2−b)+11=7F; for a81 \left( a ^ { 2 } - b \right) + 11 = 7 F ; \text { for } a81(a2−b)+11=7F; for a

Solve for the Specified Variable $81 \left( a ^ { 2 } - b \right) + 11 = 7 F ; \text { for } a$