Question

1. solve for x:

\sqrt{x + 58} - 9 = -2

Explanation:

Step1: Isolate the square root term

Add 9 to both sides of the equation:
$\sqrt{x + 58}-9 + 9=-2 + 9$
Simplify to get:
$\sqrt{x + 58}=7$

Step2: Eliminate the square root

Square both sides of the equation:
$(\sqrt{x + 58})^2=7^2$
Which simplifies to:
$x + 58 = 49$

Step3: Solve for x

Subtract 58 from both sides:
$x+58 - 58=49 - 58$
Simplify to find:
$x=-9$

Step4: Check the solution

Substitute $x = - 9$ into the original equation:
Left - hand side: $\sqrt{-9 + 58}-9=\sqrt{49}-9 = 7-9=-2$
Right - hand side: $-2$
Since the left - hand side equals the right - hand side, $x=-9$ is a valid solution.

Answer:

$x = - 9$