SOLUTION: Can you help me figure out what the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x2 + 3x + 7. I know I can graph it to find the answers, but I am not sur

Algebra ->  Functions -> SOLUTION: Can you help me figure out what the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x2 + 3x + 7. I know I can graph it to find the answers, but I am not sur      Log On


   

Question 857325: Can you help me figure out what the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x2 + 3x + 7. I know I can graph it to find the answers, but I am not sure how to even work the problem out to get to the graphing.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
0 = -3x2 + 3x + 7

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve -3%2Ax%5E2%2B3%2Ax%2B7=0 ( notice a=-3, b=3, and c=7)





x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A-3%2A7+%29%29%2F%282%2A-3%29 Plug in a=-3, b=3, and c=7




x+=+%28-3+%2B-+sqrt%28+9-4%2A-3%2A7+%29%29%2F%282%2A-3%29 Square 3 to get 9




x+=+%28-3+%2B-+sqrt%28+9%2B84+%29%29%2F%282%2A-3%29 Multiply -4%2A7%2A-3 to get 84




x+=+%28-3+%2B-+sqrt%28+93+%29%29%2F%282%2A-3%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-3+%2B-+sqrt%2893%29%29%2F%282%2A-3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-3+%2B-+sqrt%2893%29%29%2F-6 Multiply 2 and -3 to get -6


So now the expression breaks down into two parts


x+=+%28-3+%2B+sqrt%2893%29%29%2F-6 or x+=+%28-3+-+sqrt%2893%29%29%2F-6



Now break up the fraction



x=-3%2F-6%2Bsqrt%2893%29%2F-6 or x=-3%2F-6-sqrt%2893%29%2F-6



Simplify



x=1%2F2-sqrt%2893%29%2F6 or x=1%2F2%2Bsqrt%2893%29%2F6



So the solutions are:

x=1%2F2-sqrt%2893%29%2F6 or x=1%2F2%2Bsqrt%2893%29%2F6



x = 1/6 (3-sqrt(93)) x = -1.1073
x = 1/6 (3+sqrt(93)) x = 2.1073