SOLUTION: Solve using quadratic formula. Having trouble any help appreciated. 5x^2+x=3 Thanks,

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve using quadratic formula. Having trouble any help appreciated. 5x^2+x=3 Thanks,      Log On


   

Question 89170: Solve using quadratic formula. Having trouble any help appreciated.
5x^2+x=3
Thanks,
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2%2Bx=3

5x%5E2%2Bx-3=0 Subtract 3 from both sides

Now 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 5%2Ax%5E2%2Bx-3=0 ( notice a=5, b=1, and c=-3)

x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A5%2A-3+%29%29%2F%282%2A5%29 Plug in a=5, b=1, and c=-3



x+=+%28-1+%2B-+sqrt%28+1-4%2A5%2A-3+%29%29%2F%282%2A5%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B60+%29%29%2F%282%2A5%29 Multiply -4%2A-3%2A5 to get 60



x+=+%28-1+%2B-+sqrt%28+61+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+sqrt%2861%29%29%2F%282%2A5%29 Simplify the square root



x+=+%28-1+%2B-+sqrt%2861%29%29%2F10 Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

x+=+%28-1+%2B+sqrt%2861%29%29%2F10 or x+=+%28-1+-+sqrt%2861%29%29%2F10


which split up to


x=-1%2F10%2Bsqrt%2861%29%2F10 or x=-1%2F10-sqrt%2861%29%2F10


Which approximate to

x=0.681024967590665 or x=-0.881024967590665


So our solutions are:
x=0.681024967590665 or x=-0.881024967590665

Notice when we graph 5%2Ax%5E2%2Bx-3, we get:



when we use the root finder feature on a calculator, we find that x=0.681024967590665 and x=-0.881024967590665.So this verifies our answer