Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −5y^2 + 2y = −2

Answer 1

So before we can solve using the quadratic formula, we have to set the equation to zero. We can do that by adding 2 on both sides of the equation
`-5y^2 + 2y +2 =0`

Now we can use the quadratic formula, which is
`y=(-b+√(b^2-4ac))/(2a),(-b-√(b^2-4ac))/(2a)` , with a=x^2 coefficient, b=x coefficient, and c=constant. We can form the equation as such:
`y=(-2+√(2^2-4*(-5)*2))/(2*(-5)),(-2-√(2^2-4*(-5)*2))/(2*(-5))`

Firstly, solve the exponents and the multiplications:
`y=(-2+√(4+40))/(-10),(-2-√(4+40))/(-10)`

Next, do the addition within the radicals (these will be your exact solutions. but I'll solve for the decimal form as well.):
`y=(-2+√(44))/(-10),(-2-√(44))/(-10)`

Next, solve for the rest on your calculator, and your answers will be (rounded to the thousandths) y = -0.463, 0.863