To solve the quadratic equation 0 = -5x^2 + 3x + 2, you can use the quadratic formula or factorization method.
1. Using the quadratic formula:
The quadratic formula states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In your case, the quadratic equation is -5x^2 + 3x + 2 = 0, so a = -5, b = 3, and c = 2. Plugging these values into the quadratic formula, we get:
x = (-3 ± √(3^2 - 4*(-5)*2)) / (2*(-5))
x = (-3 ± √(9 + 40)) / -10
x = (-3 ± √49) / -10
x = (-3 ± 7) / -10
This results in two solutions:
x = (-3 + 7) / -10 = 4 / -10 = -0.4
x = (-3 - 7) / -10 = -10 / -10 = 1
Therefore, the solutions to the quadratic equation -5x^2 + 3x + 2 = 0 are x = -0.4 and x = 1.
2. Using factoring:
Another method to solve the quadratic equation is by factoring. You would factor the quadratic equation and set each factor equal to zero:
-5x^2 + 3x + 2 = 0
(-5x + 2)(x + 1) = 0
From this factored form, you get:
-5x + 2 = 0 -> -5x = -2 -> x = -2/5
x + 1 = 0 -> x = -1
Therefore, the solutions using factoring are x = -2/5 and x = -1.