solve -2x^2 + 3x - 1 = -2 using the quadratic formula. round the solutions to the nearest hundredths. Enter the small solution first
To solve the equation -2x^2 + 3x - 1 = -2 using the quadratic formula, we need to rearrange the equation into the form ax^2 + bx + c = 0.
So, -2x^2 + 3x - 1 + 2 = 0
-2x^2 + 3x + 1 = 0
Now, we can identify that a = -2, b = 3, and c = 1.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values, we get:
x = (-3 ± √(3^2 - 4(-2)(1))) / (2(-2))
Simplifying further:
x = (-3 ± √(9 + 8)) / (-4)
x = (-3 ± √17) / (-4)
Now, we can find the two solutions by rounding them to the nearest hundredths.
First, let's consider the "+" case:
x1 = (-3 + √17) / (-4) ≈ 0.83
Next, let's consider the "-" case:
x2 = (-3 - √17) / (-4) ≈ -0.33
Therefore, the solution to the equation -2x^2 + 3x - 1 = -2 using the quadratic formula (rounded to the nearest hundredths) is:
x ≈ -0.33, 0.83