Solve $x = \sqrt { 56 - x }$ , if possible.
A) x=8
B) x=56
C) x=7
D) x=-7
E)no solution

Question

Quizplus · Accepted Answer

First, we square both sides of the equation in order to eliminate the square root:
\begin{align*}
x &= \sqrt { 56 - x } \
x^2 &= 56 - x \
x^2 + x - 56 &= 0 \
(x + 8)(x - 7) &= 0
\end{align*}
Solving the quadratic equation we have, 
$$x=-8	ext{ or }x=7$$
Our answer must satisfy the original equation.

Checking $x=-8$ we find that $\sqrt{56-x}=\sqrt{64}$ which is 8 so the equation is false.

Checking $x=7$ we have $\sqrt{56-x}=\sqrt{49}=7$ so $7=\sqrt{56-7}$. Thus, $x=7$ is the solution to the equation.

Solve x=56−xx = \sqrt { 56 - x }x=56−x​ , If Possible

Solve $x = \sqrt { 56 - x }$ , If Possible