solve the following equation by using the quadratic formula. please show all your work to receive full credit.
-3x^2 + 10x - 3 = 0
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation: -3x^2 + 10x - 3 = 0
we have:
a = -3
b = 10
c = -3
Plugging these values in the quadratic formula, we get:
x = (-(10) ± √((10)^2 - 4(-3)(-3))) / (2(-3))
simplifying further:
x = (-10 ± √(100 - 36)) / -6
x = (-10 ± √64) / -6
Taking the square root of 64, we get:
x = (-10 ± 8) / -6
Now, we can solve for x by evaluating both the plus and minus cases:
Case 1: When x = (-10 + 8) / -6
x = -2 / -6
x = 1/3
Case 2: When x = (-10 - 8) / -6
x = -18 / -6
x = 3
Therefore, the solutions to the given equation are x = 1/3 and x = 3.