Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth.
5y^2 - 8y = 2
To solve the equation 5y^2 - 8y = 2 using the quadratic formula, we first rearrange the equation to the form ax^2 + bx + c = 0:
5y^2 - 8y - 2 = 0
Comparing this equation to the general form ax^2 + bx + c = 0, we have a = 5, b = -8, and c = -2.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the quadratic formula, we have:
y = (-(-8) ± √((-8)^2 - 4 * 5 * -2)) / (2 * 5)
Simplifying further:
y = (8 ± √(64 + 40)) / 10
y = (8 ± √(104)) / 10
We can round the answer to the nearest hundredth:
y ≈ (8 ± 10.2) / 10
This gives us two possible solutions:
y ≈ (8 + 10.2) / 10 ≈ 1.02
y ≈ (8 - 10.2) / 10 ≈ -0.22
Therefore, the solutions to the equation 5y^2 - 8y = 2 are y ≈ 1.02 and y ≈ -0.22.