Question

4 multiple choice 1 point
what is the correct first step in solving the equation $x - 6 = \sqrt{x^2 + 58}$?
$square$ square both sides of the equation to get $(x - 6)^2 = x^2 + 58$
$square$ square both sides of the equation to get $x - 6 = x^2 + 58$
$square$ subtract 58 from both sides of the equation to get $x - 64 = \sqrt{x^2}$
$square$ add 6 to both sides of the equation to get $x = \sqrt{x^2 + 64}$
clear my selection

Explanation:

Step1: Analyze radical equation solving

To eliminate the square root, the standard first step for an equation with a single radical on one side is to isolate the radical (it is already isolated here: $\sqrt{x^2+58}$ is alone on the right) and then square both sides to remove the square root.

Step2: Verify correct squaring operation

When squaring the left side $x-6$, we must square the entire expression, so $(x-6)^2$. Squaring the right side $\sqrt{x^2+58}$ gives $x^2+58$. So the correct first step is squaring both sides to get $(x-6)^2 = x^2+58$.

Answer:

A. Square both sides of the equation to get $(x - 6)^2 = x^2 + 58$