Quadratic Formula A794Dc

1. The user mentioned several algebra topics: Algebraic Expressions, Simultaneous Equations, Quadratic Formula, Completing the square, and Factorization. 2. Since no specific problem was given, I will explain the Quadratic Formula as it is a common and important topic. 3. Problem: Solve the quadratic equation $$ax^2 + bx + c = 0$$ using the Quadratic Formula. 4. Formula: The Quadratic Formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 5. Explanation: This formula gives the solutions (roots) of any quadratic equation where $$a \neq 0$$. 6. Steps to solve: 1. Identify coefficients $$a$$, $$b$$, and $$c$$ from the quadratic equation. 2. Calculate the discriminant $$\Delta = b^2 - 4ac$$. 3. If $$\Delta > 0$$, there are two real and distinct roots. 4. If $$\Delta = 0$$, there is one real root (a repeated root). 5. If $$\Delta < 0$$, there are two complex roots. 7. Example: Solve $$2x^2 - 4x - 6 = 0$$. 1. Here, $$a=2$$, $$b=-4$$, $$c=-6$$. 2. Calculate discriminant: $$\Delta = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$. 3. Since $$\Delta = 64 > 0$$, two real roots exist. 4. Apply formula: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$. 5. Calculate roots: $$x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$$ $$x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$$ 8. Final answer: The solutions are $$x=3$$ and $$x=-1$$.