Solve the Equation: Combining Like Terms in x² + x² - 3 = x² + 6

To solve this problem, we'll follow these steps:

• Simplify the given equation.
• Solve for $x^2$ and find $x$.

First, let's simplify the equation:

$x^2 + x^2 - 3 = x^2 + 6$.

Combine like terms on the left side:

$2x^2 - 3 = x^2 + 6$.

Subtract $x^2$ from both sides to isolate one of the $x$ terms:

$2x^2 - x^2 - 3 = 6$.

This simplifies to:

$x^2 - 3 = 6$.

Next, add 3 to both sides to solve for $x^2$:

$x^2 = 9$.

To find $x$, take the square root of both sides:

$x = \pm\sqrt{9}$.

This results in:

$x = \pm3$.

Therefore, the solution to the problem is $\pm3$.