SOLUTION: Solve x^2 + 7x -2 = 0 And, then find the x-intercepts of f(x) = x^2 + 7x - 2. I appreciate the help, I am struggling with these problems and they do not come from a textbook.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve x^2 + 7x -2 = 0 And, then find the x-intercepts of f(x) = x^2 + 7x - 2. I appreciate the help, I am struggling with these problems and they do not come from a textbook.      Log On


   

Question 130767: Solve x^2 + 7x -2 = 0
And, then find the x-intercepts of f(x) = x^2 + 7x - 2.
I appreciate the help, I am struggling with these problems and they do not come from a textbook.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


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 x%5E2%2B7%2Ax-2=0 ( notice a=1, b=7, and c=-2)




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



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



x+=+%28-7+%2B-+sqrt%28+49%2B8+%29%29%2F%282%2A1%29 Multiply -4%2A-2%2A1 to get 8



x+=+%28-7+%2B-+sqrt%28+57+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)





x+=+%28-7+%2B-+sqrt%2857%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-7+%2B+sqrt%2857%29%29%2F2 or x+=+%28-7+-+sqrt%2857%29%29%2F2



So these expressions approximate to

x=0.274917217635375 or x=-7.27491721763537


So our solutions are:
x=0.274917217635375 or x=-7.27491721763537

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



when we use the root finder feature on a calculator, we find that x=0.274917217635375 and x=-7.27491721763537.So this verifies our answer