Subjects algebra

Quadratic Formula Ec7D82

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1. **State the problem:** Solve the quadratic equation using the quadratic formula and express the solution set in exact simplest form. 2. **Recall the quadratic formula:** For a quadratic equation $ax^2 + bx + c = 0$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Identify coefficients:** Identify $a$, $b$, and $c$ from the given quadratic equation. 4. **Calculate the discriminant:** Compute $\Delta = b^2 - 4ac$. 5. **Evaluate the square root:** Simplify $\sqrt{\Delta}$ as much as possible. 6. **Apply the quadratic formula:** Substitute $a$, $b$, and $\sqrt{\Delta}$ into the formula. 7. **Simplify the expression:** If possible, factor and cancel common factors using the cancellation notation: $$x = \frac{\cancel{-b} \pm \sqrt{\cancel{b^2} - 4\cancel{a}c}}{2\cancel{a}}$$ 8. **Write the solution set:** Express the solutions in exact simplest form. Since the specific quadratic equation was not provided, this is the general method to solve any quadratic equation using the quadratic formula.