1. Stating the problem: Simplify or analyze the expression $$4x^2 - 7$$. 2. This is a quadratic expression where the variable $x$ is squared and multiplied by 4, and then 7 is subtracted from the result. 3. There is no further simplification since the terms are unlike terms. 4. If solving for roots, set the expression equal to zero: $$4x^2 - 7 = 0$$. 5. Add 7 to both sides: $$4x^2 = 7$$. 6. Divide both sides by 4: $$x^2 = \frac{7}{4}$$. 7. Take the square root of both sides: $$x = \pm \sqrt{\frac{7}{4}} = \pm \frac{\sqrt{7}}{2}$$. Final answer: The roots of the equation $$4x^2 - 7 = 0$$ are $$x = \pm \frac{\sqrt{7}}{2}$$.