Answer :

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.