Question

1. $4x^2 - 6 = 394$

$+6$ $+6$
$\frac{4x^2}{4x} = \frac{400}{4}$

Explanation:

Step1: Solve for \(4x^2\)

Add 6 to both sides of the equation \(4x^2 - 6 = 394\).
\(4x^2 - 6 + 6 = 394 + 6\)
\(4x^2 = 400\)

Step2: Solve for \(x^2\)

Divide both sides by 4.
\(\frac{4x^2}{4}=\frac{400}{4}\)
\(x^2 = 100\)

Step3: Solve for \(x\)

Take the square root of both sides. Remember that a square root has two solutions (positive and negative).
\(x=\pm\sqrt{100}\)
\(x = \pm 10\)

Answer:

\(x = 10\) or \(x = -10\) (or in boxed form, if needed for a single answer context, but since it's two solutions, \(\pm 10\))