Answer: x = -1/2 and x = -1
Step-by-step explanation: To solve the quadratic equation 2x^2 + 3x + 1 = 0 using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), where a = 2, b = 3, and c = 1, follow these steps:
1. Identify the values of a, b, and c.
- a = 2
- b = 3
- c = 1
2. Substitute these values into the quadratic formula:
x = (-3 ± √(3^2 - 4 * 2 * 1)) / (2 * 2)
3. Calculate the discriminant (b^2 - 4ac):
b^2 - 4ac = 3^2 - 4 * 2 * 1 = 9 - 8 = 1
4. Substitute the discriminant into the quadratic formula:
x = (-3 ± √1) / 4
5. Simplify the square root of the discriminant:
√1 = 1
6. Substitute the simplified square root back into the formula:
x = (-3 ± 1) / 4
7. Split the equation into two possible solutions:
x₁ = (-3 + 1) / 4 = -2/4 = -1/2
x₂ = (-3 - 1) / 4 = -4/4 = -1
So, the solutions to the equation 2x^2 + 3x + 1 = 0 using the quadratic formula are x = -1/2 and x = -1.