Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth.
-5y^2 + 2y = -2
The given quadratic equation is: -5y^2 + 2y = -2
First, we need to rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, rearranging the terms, we get:
-5y^2 + 2y + 2 = 0
Now, we can use the quadratic formula to solve for y. The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = -5, b = 2, and c = 2. Substituting these values into the quadratic formula:
y = (-2 ± √(2^2 - 4(-5)(2))) / (2(-5))
Simplifying further:
y = (-2 ± √(4 + 40)) / -10
y = (-2 ± √44) / -10
Now, we evaluate both options for y:
y = (-2 + √44) / -10, and
y = (-2 - √44) / -10
Using a calculator to find the square root of 44: √44 ≈ 6.63
y = (-2 + 6.63) / -10
y = 4.63 / -10
y ≈ -0.46
y = (-2 - 6.63) / -10
y = -8.63 / -10
y ≈ 0.86
Therefore, the solutions to the equation -5y^2 + 2y = -2 are approximately y = -0.46 and y = 0.86.