1. Let's start with the equation given: $$2x^2 + 2x^2 = (ab)^2$$ 2. Combine like terms on the left side: $$2x^2 + 2x^2 = 4x^2$$ So the equation becomes: $$4x^2 = (ab)^2$$ 3. To solve for $x^2$, divide both sides by 4: $$x^2 = \frac{(ab)^2}{4}$$ 4. To get $x$, take the square root of both sides: $$x = \pm \frac{ab}{2}$$ This means $x$ is equal to positive or negative $\frac{ab}{2}$. Final answer: $$x = \pm \frac{ab}{2}$$