SOLUTION: Solve the following using the square root method or the quadratic equation. 66x^2 -31x -9 + 0 Not understanding this can you help Please!! Thanks

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following using the square root method or the quadratic equation. 66x^2 -31x -9 + 0 Not understanding this can you help Please!! Thanks      Log On


   

Question 87266: Solve the following using the square root method or the quadratic equation.
66x^2 -31x -9 + 0
Not understanding this can you help Please!!
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the general quadratic

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

the general form of the quadratic equation is:

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

So lets solve 66%2Ax%5E2-31%2Ax-9=0

x+=+%2831+%2B-+sqrt%28+%28-31%29%5E2-4%2A66%2A-9+%29%29%2F%282%2A66%29 Plug in a=66, b=-31, and c=-9



x+=+%2831+%2B-+sqrt%28+961-4%2A66%2A-9+%29%29%2F%282%2A66%29 Square -31 to get 961



x+=+%2831+%2B-+sqrt%28+961%2B2376+%29%29%2F%282%2A66%29 Multiply -4%2A-9%2A66 to get 2376



x+=+%2831+%2B-+sqrt%28+3337+%29%29%2F%282%2A66%29 Combine like terms in the radicand (everything under the square root)



x+=+%2831+%2B-+sqrt%283337%29%29%2F%282%2A66%29 Simplify the square root



x+=+%2831+%2B-+sqrt%283337%29%29%2F132 Multiply 2 and 66 to get 132

So now the expression breaks down into two parts

x+=+%2831+%2B+sqrt%283337%29%29%2F132 or x+=+%2831+-+sqrt%283337%29%29%2F132


Which approximate to

x=0.672475548910187 or x=-0.202778579213218


So our solutions are:
x=0.672475548910187 or x=-0.202778579213218

Notice when we graph 66%2Ax%5E2-31%2Ax-9 we get:



when we use the root finder feature on a calculator, we find that x=0.672475548910187 and x=-0.202778579213218.So this verifies our answer