Quadratic Solutions Bcbf44

1. **State the problem:** Solve the quadratic equation $$2x^2+7x+4=8$$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$2x^2 + 7x + 4 - 8 = 0$$ which simplifies to $$2x^2 + 7x - 4 = 0$$ 3. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 4. **Identify coefficients:** Here, $$a=2$$, $$b=7$$, and $$c=-4$$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 7^2 - 4 \times 2 \times (-4) = 49 + 32 = 81$$ 6. **Calculate the square root of the discriminant:** $$\sqrt{81} = 9$$ 7. **Apply the quadratic formula:** $$x = \frac{-7 \pm 9}{2 \times 2} = \frac{-7 \pm 9}{4}$$ 8. **Find the two solutions:** - For the plus sign: $$x = \frac{-7 + 9}{4} = \frac{2}{4} = 0.5$$ - For the minus sign: $$x = \frac{-7 - 9}{4} = \frac{-16}{4} = -4$$ 9. **Final answer:** The solutions are $$x = 0.5$$ and $$x = -4$$. 10. **Match with given options:** The correct choice is **x = -4 and x = 0.5**.