Solve the equation. Check all solutions. $\sqrt { x - 6 } - 4 = 5$
A)85
B)64
C)87
D)76
E)no solution

Question

Quizplus · Accepted Answer

First, we isolate the square root term by adding 4 to both sides of the equation:

\begin{align*}
\sqrt{x-6} &= 9 \
\end{align*}

Next, we square both sides of the equation:

\begin{align*}
(\sqrt{x-6})^2 &= 9^2 \
x-6 &= 81 \
x &= 87 \
\end{align*}

Therefore, the solution to the equation is x = 87. We can check this solution by plugging it back into the original equation:

\begin{align*}
\sqrt{x-6} - 4 &= 5 \
\sqrt{87-6} - 4 &= 5 \
\sqrt{81} - 4 &= 5 \
9 - 4 &= 5 \
5 &= 5 \
\end{align*}

Since both sides of the equation are equal when x = 87, we can conclude that x = 87 is the correct solution.

Solve the Equation x−6−4=5\sqrt { x - 6 } - 4 = 5x−6​−4=5