Solve using the quadratic formula.
–2d^2 − 5d + 6 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
We can solve –2d^2 − 5d + 6 = 0 using the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, the coefficients are: a = -2, b = -5, and c = 6. Substituting these values into the formula, we get:
d = (-(-5) ± √((-5)^2 - 4(-2)(6))) / 2(-2)
d = (5 ± √(25 + 48)) / -4
d = (5 ± √73) / -4
So, the solutions are:
d = (5 + √73) / -4
d = (5 - √73) / -4
These are the exact solutions. If you prefer decimal approximations, they are approximately:
d ≈ -0.52
d ≈ 2.77