SOLUTION: I can not find the solutions to this problem please help with a way i can come to the answer 2x^2+11x-1=0 thank you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I can not find the solutions to this problem please help with a way i can come to the answer 2x^2+11x-1=0 thank you       Log On


   

Question 96922: I can not find the solutions to this problem please help with a way i can come to the answer 2x^2+11x-1=0 thank you
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2+11x-1
Use the quadratic formula
a=2; b=11; c=-1
x = [-b +- sqrt(b^2-4ac)]/(2a)
Your problem:
x = [-11 +- sqrt(121-4*2*-1)]/(2*2)
x = [-11 +- sqrt(129)]/4
x = [-11 + sqrt(129)]/4 or x = [-11 - sqrt(129)]/4
===============
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 2%2Ax%5E2%2B11%2Ax-1=0 ( notice a=2, b=11, and c=-1)

x+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29 Plug in a=2, b=11, and c=-1



x+=+%28-11+%2B-+sqrt%28+121-4%2A2%2A-1+%29%29%2F%282%2A2%29 Square 11 to get 121



x+=+%28-11+%2B-+sqrt%28+121%2B8+%29%29%2F%282%2A2%29 Multiply -4%2A-1%2A2 to get 8



x+=+%28-11+%2B-+sqrt%28+129+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-11+%2B-+sqrt%28129%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-11+%2B-+sqrt%28129%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%28-11+%2B+sqrt%28129%29%29%2F4 or x+=+%28-11+-+sqrt%28129%29%29%2F4


Now break up the fraction


x=-11%2F4%2Bsqrt%28129%29%2F4 or x=-11%2F4-sqrt%28129%29%2F4


Simplify


x=-11+%2F+4%2Bsqrt%28129%29%2F4 or x=-11+%2F+4-sqrt%28129%29%2F4


So these expressions approximate to

x=0.0894541729001368 or x=-5.58945417290014


So our solutions are:
x=0.0894541729001368 or x=-5.58945417290014

Notice when we graph 2%2Ax%5E2%2B11%2Ax-1, we get:



when we use the root finder feature on a calculator, we find that x=0.0894541729001368 and x=-5.58945417290014.So this verifies our answer