The problem is to solve the equation $4x^2 - 3^2 = 10$ for $x$.

1. Problem Description

The problem is to solve the equation $4x^2 - 3^2 = 10$ for $x$.

2. Solution Steps

First, we simplify the equation:

$4x^2 - 3^2 = 10$

$4x^2 - 9 = 10$

Next, we add 9 to both sides of the equation:

$4x^2 - 9 + 9 = 10 + 9$

$4x^2 = 19$

Then, we divide both sides of the equation by 4:

$\frac{4x^2}{4} = \frac{19}{4}$

$x^2 = \frac{19}{4}$

Now, we take the square root of both sides of the equation:

$\sqrt{x^2} = \pm\sqrt{\frac{19}{4}}$

$x = \pm\frac{\sqrt{19}}{\sqrt{4}}$

$x = \pm\frac{\sqrt{19}}{2}$

3. Final Answer

$x = \frac{\sqrt{19}}{2}$ or $x = -\frac{\sqrt{19}}{2}$