SOLUTION: I知 really confused with this; please help me solve this problem. a) Solve x^2+7x-1=0 b) Find the x-intercepts of f(f) =x^2+7x-1 What are the solutions? X=? (Type exact answer

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I知 really confused with this; please help me solve this problem. a) Solve x^2+7x-1=0 b) Find the x-intercepts of f(f) =x^2+7x-1 What are the solutions? X=? (Type exact answer      Log On


   

Question 217145: I知 really confused with this; please help me solve this problem.
a) Solve x^2+7x-1=0
b) Find the x-intercepts of f(f) =x^2+7x-1
What are the solutions?
X=?
(Type exact answers, using radicals as needed. Use a comma to separate answers as needed)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a) Solve x^2+7x-1=0
b) Find the x-intercepts of f(f) =x^2+7x-1
That's the same function twice (assuming you mean f(x))
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%287%29%5E2-4%2A1%2A-1=53.

Discriminant d=53 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+53+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+53+%29%29%2F2%5C1+=+0.140054944640259
x%5B2%5D+=+%28-%287%29-sqrt%28+53+%29%29%2F2%5C1+=+-7.14005494464026

Quadratic expression 1x%5E2%2B7x%2B-1 can be factored:
1x%5E2%2B7x%2B-1+=+%28x-0.140054944640259%29%2A%28x--7.14005494464026%29
Again, the answer is: 0.140054944640259, -7.14005494464026. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-1+%29

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x = (-7 + sqrt(53))/2
x = (-7 - sqrt(53))/2