Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth.

Question

5y^2 - 8y = 2

Answer 1

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.