Question

1. $4x^2 - 30 = 22$

Explanation:

Step1: Isolate the \(x^2\) term

Add 30 to both sides of the equation \(4x^2 - 30 = 22\):
\(4x^2 - 30 + 30 = 22 + 30\)
\(4x^2 = 52\)

Step2: Solve for \(x^2\)

Divide both sides by 4:
\(\frac{4x^2}{4}=\frac{52}{4}\)
\(x^2 = 13\)

Step3: Solve for \(x\)

Take the square root of both sides. Remember that when taking the square root of a number, we consider both the positive and negative roots:
\(x=\pm\sqrt{13}\)

Answer:

\(x = \sqrt{13}\) or \(x = -\sqrt{13}\) (or approximately \(x\approx3.6055\) or \(x\approx - 3.6055\))