Answer:
To solve the equation 5x^2 - 5x - 2 = 0 to the nearest hundredth, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 5, b = -5, and c = -2. Plugging these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(5)(-2))) / (2(5))
x = (5 ± √(25 + 40)) / 10
x = (5 ± √65) / 10
So the solutions to the equation are:
x ≈ (5 + √65) / 10 and x ≈ (5 - √65) / 10
Rounding these to the nearest hundredth, we get:
x ≈ 1.61 and x ≈ -0.61
