SOLUTION: What is the solution for {{{2x^2+7x+1=0}}} using the quadratic formula? Please explain how you got the answer in steps.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: What is the solution for {{{2x^2+7x+1=0}}} using the quadratic formula? Please explain how you got the answer in steps.      Log On


   

Question 120363: What is the solution for 2x%5E2%2B7x%2B1=0 using the quadratic formula? Please explain how you got the answer in steps.
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%2B7%2Ax%2B1=0 ( notice a=2, b=7, and c=1)




x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 Plug in a=2, b=7, and c=1



x+=+%28-7+%2B-+sqrt%28+49-4%2A2%2A1+%29%29%2F%282%2A2%29 Square 7 to get 49



x+=+%28-7+%2B-+sqrt%28+49%2B-8+%29%29%2F%282%2A2%29 Multiply -4%2A1%2A2 to get -8



x+=+%28-7+%2B-+sqrt%28+41+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-7+%2B-+sqrt%2841%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+=+%28-7+%2B-+sqrt%2841%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%28-7+%2B+sqrt%2841%29%29%2F4 or x+=+%28-7+-+sqrt%2841%29%29%2F4


Now break up the fraction


x=-7%2F4%2Bsqrt%2841%29%2F4 or x=-7%2F4-sqrt%2841%29%2F4





So these expressions approximate to

x=-0.149218940641788 or x=-3.35078105935821


So our solutions are:
x=-0.149218940641788 or x=-3.35078105935821

Notice when we graph 2%2Ax%5E2%2B7%2Ax%2B1, we get:



when we use the root finder feature on a calculator, we find that x=-0.149218940641788 and x=-3.35078105935821.So this verifies our answer