How can I solve the equation 2x^2 + 40x + 2 = 0?

To solve the quadratic equation 2x² + 40x + 2 = 0, we can use the quadratic formula, which is given by:

x = (-b ± √(b² – 4ac)) / 2a

Here, the coefficients are:

• a = 2
• b = 40
• c = 2

Now, we will calculate the discriminant, which is b² – 4ac:

b² = 40² = 1600

4ac = 4 * 2 * 2 = 16

Now, finding the discriminant:

b² – 4ac = 1600 – 16 = 1584

Since the discriminant is positive, we can conclude that there are two distinct real solutions. Next, we will substitute these values into the quadratic formula:

x = (-40 ± √1584) / (2 * 2)

Calculating the square root:

√1584 ≈ 39.8

Now, substituting this back:

x = (-40 ± 39.8) / 4

This will give us two solutions:

1. x = (-40 + 39.8) / 4 = -0.05

2. x = (-40 – 39.8) / 4 = -19.95

Thus, the solutions to the equation 2x² + 40x + 2 = 0 are:

• x ≈ -0.05
• x ≈ -19.95

Feel free to ask if you need further clarification on solving quadratic equations!