Question

im2 midterm study guide #2
test overview 4
question 11
solve for x in the equation $x^2 - 5 = -1$.
answer
$x = 2$
$x = 4, -4$
no real solution
$x = 2, -2$

Explanation:

Step1: Isolate \(x^2\)

Add 5 to both sides of the equation \(x^2 - 5 = -1\):
\(x^2 - 5 + 5 = -1 + 5\)
Simplify: \(x^2 = 4\)

Step2: Solve for \(x\)

Take the square root of both sides. Remember, square roots have two solutions (positive and negative):
\(x = \pm\sqrt{4}\)
Simplify: \(x = 2\) or \(x = -2\)

Answer:

\(x = 2, -2\) (corresponding to the option "x = 2, -2")