How do you solve 5x² - 2x - 2 = 0?

To solve the quadratic equation 5x² - 2x - 2 = 0, you can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

In this formula, a, b, and c are the coefficients from the equation ax² + bx + c = 0. For your equation:

• a = 5
• b = -2
• c = -2

Now, plug these values into the formula:

Step 1: Calculate the Discriminant

The discriminant is b² - 4ac. Let's calculate it:

• b² = (-2)² = 4
• 4ac = 4 × 5 × (-2) = -40
• Discriminant = 4 - (-40) = 4 + 40 = 44

Step 2: Apply the Quadratic Formula

Now substitute the values into the quadratic formula:

• x = [2 ± √44] / (2 × 5)
• x = [2 ± 2√11] / 10

Step 3: Simplify the Expression

This gives us two possible solutions:

• x = (2 + 2√11) / 10
• x = (2 - 2√11) / 10

Finally, you can simplify these further:

• x = (1 + √11) / 5
• x = (1 - √11) / 5

These are the two solutions to the equation 5x² - 2x - 2 = 0.