SOLUTION: I am lost. If anyone can help I would appreciate it. Thanks Solve x^2+7x-1=0 Find the x intercepts of f(x)=x^2+7x-1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I am lost. If anyone can help I would appreciate it. Thanks Solve x^2+7x-1=0 Find the x intercepts of f(x)=x^2+7x-1      Log On


   

Question 129694: I am lost. If anyone can help I would appreciate it. Thanks
Solve
x^2+7x-1=0
Find the x intercepts of
f(x)=x^2+7x-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
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-1=0 ( notice a=1, b=7, and c=-1)





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




x+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A-1+%29%29%2F%282%2A1%29 Square 7 to get 49




x+=+%28-7+%2B-+sqrt%28+49%2B4+%29%29%2F%282%2A1%29 Multiply -4%2A-1%2A1 to get 4




x+=+%28-7+%2B-+sqrt%28+53+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-7+%2B-+sqrt%2853%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-7+%2B-+sqrt%2853%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-7+%2B+sqrt%2853%29%29%2F2 or x+=+%28-7+-+sqrt%2853%29%29%2F2



Now break up the fraction



x=-7%2F2%2Bsqrt%2853%29%2F2 or x=-7%2F2-sqrt%2853%29%2F2



Simplify



x=-7%2F2%2Bsqrt%2853%29%2F2 or x=-7%2F2-sqrt%2853%29%2F2



So the solutions are:

x=-7%2F2%2Bsqrt%2853%29%2F2 or x=-7%2F2-sqrt%2853%29%2F2