Answer: x = -1/2 and x = -7.
Explanation:
To solve the equation 2x^2 + 15x + 7 = 0 using the quadratic formula, we can follow these steps:
1. Identify the values of a, b, and c in the equation ax^2 + bx + c = 0.
In this case, a = 2, b = 15, and c = 7.
2. Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
3. Calculate the discriminant, which is the expression inside the square root:
discriminant = b^2 - 4ac
4. Plug the values of a, b, and c into the discriminant formula:
discriminant = 15^2 - 4 * 2 * 7
5. Simplify the expression to find the discriminant:
discriminant = 225 - 56
discriminant = 169
6. Determine the value of the square root of the discriminant:
√(169) = 13
7. Now, we can apply the quadratic formula using the values we have calculated:
x = (-15 ± 13) / (2 * 2)
8. Simplify the expression inside the parentheses:
x = (-15 + 13) / 4 or x = (-15 - 13) / 4
9. Calculate the solutions:
x = -2 / 4 or x = -28 / 4
10. Simplify the solutions:
x = -1/2 or x = -7
So, the solutions to the equation 2x^2 + 15x + 7 = 0 using the quadratic formula are x = -1/2 and x = -7.