SOLUTION: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state. 3x^2 + x - 3 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state. 3x^2 + x - 3 = 0      Log On


   

Question 248210: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state.
3x^2 + x - 3 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Bx-3=0 ( notice a=3, b=1, and c=-3)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A3%2A-3+%29%29%2F%282%2A3%29 Plug in a=3, b=1, and c=-3




x+=+%28-1+%2B-+sqrt%28+1-4%2A3%2A-3+%29%29%2F%282%2A3%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B36+%29%29%2F%282%2A3%29 Multiply -4%2A-3%2A3 to get 36




x+=+%28-1+%2B-+sqrt%28+37+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+sqrt%2837%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+sqrt%2837%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%28-1+%2B+sqrt%2837%29%29%2F6 or x+=+%28-1+-+sqrt%2837%29%29%2F6



Now break up the fraction



x=-1%2F6%2Bsqrt%2837%29%2F6 or x=-1%2F6-sqrt%2837%29%2F6



Simplify



x=-1%2F6%2Bsqrt%2837%29%2F6 or x=-1%2F6-sqrt%2837%29%2F6



So the solutions are:

x=-1%2F6%2Bsqrt%2837%29%2F6 or x=-1%2F6-sqrt%2837%29%2F6