Solve the following equation by using the quadratic formula. Please show all your work to receive full credit.
−3x2+10x−3=0
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(3 points)
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the equation -3x^2 + 10x - 3 = 0 as our equation (ax^2 + bx + c = 0), we can determine the values of a, b, and c:
a = -3
b = 10
c = -3
Substituting these values into the quadratic formula:
x = (-(10) ± √((10)^2 - 4(-3)(-3))) / (2(-3))
Simplifying further:
x = (-10 ± √(100 - 36)) / -6
x = (-10 ± √64) / -6
x = (-10 ± 8) / -6
There are two possible solutions:
1) x = (-10 + 8) / -6 = -2 / -6 = 1/3
2) x = (-10 - 8) / -6 = -18 / -6 = 3
The solutions to the equation -3x^2 + 10x - 3 = 0 are x = 1/3 and x = 3.