1. Let's start by stating the problem: You asked to explain "that theorem," but since the specific theorem is not mentioned, I will explain a common fundamental theorem in algebra: the Quadratic Formula Theorem. 2. The Quadratic Formula Theorem states that for any quadratic equation of the form $$ax^2 + bx + c = 0$$ where $$a \neq 0$$, the solutions for $$x$$ can be found using the formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. Important rules to remember: - The term under the square root, $$b^2 - 4ac$$, is called the discriminant. - If the discriminant is positive, there are two real solutions. - If it is zero, there is exactly one real solution. - If it is negative, there are two complex solutions. 4. To use the formula, identify $$a$$, $$b$$, and $$c$$ from your quadratic equation. 5. Substitute these values into the formula and simplify step-by-step: - Calculate the discriminant $$b^2 - 4ac$$. - Find the square root of the discriminant. - Compute $$-b \pm \sqrt{b^2 - 4ac}$$. - Divide the result by $$2a$$. 6. This process gives you the roots (solutions) of the quadratic equation. This theorem is fundamental because it provides a direct method to solve any quadratic equation, which is a common problem in algebra.