Solve the following equation by using the quadratic formula.
−3x2+10x−3=0
The given equation is -3x^2 + 10x - 3 = 0.
To solve this equation using the quadratic formula, we first identify the coefficients of x^2, x, and the constant term. In this case, a = -3, b = 10, and c = -3.
The quadratic formula states that the solutions for x can be found using the formula: x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we get: x = (-10 ± √(10^2 - 4(-3)(-3))) / (2(-3))
Simplifying further, we have: x = (-10 ± √(100 - 36)) / (-6)
x = (-10 ± √64) / (-6)
x = (-10 ± 8) / (-6)
Now, we have two possible solutions:
Solution 1: x = (-10 + 8) / (-6) = -2 / (-6) = 1/3
Solution 2: x = (-10 - 8) / (-6) = -18 / (-6) = 3
Therefore, the solutions for the equation -3x^2 + 10x - 3 = 0 are x = 1/3 and x = 3.