SOLUTION: I cant figure this one out. Please help. Solve the equation x2 + 8x – 2 = 0 using both a) The quadratic formula b) Completing the square Prepare a few sente

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I cant figure this one out. Please help. Solve the equation x2 + 8x – 2 = 0 using both a) The quadratic formula b) Completing the square Prepare a few sente      Log On


   

Question 189419: I cant figure this one out. Please help.
Solve the equation x2 + 8x – 2 = 0 using both
a) The quadratic formula
b) Completing the square


Prepare a few sentences comparing and contrasting the two methods
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
b)x%5E2%2B8x%2B16-16-2=0
:
%28x%2B4%29%5E2=18
:
x%2B4=sqrt%2818%29 and x%2B4=-sqrt%2818%29
:
x=-4%2B3sqrt%282%29 and x=-4-3sqrt%282%29
:
a)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B-2+=+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=%288%29%5E2-4%2A1%2A-2=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+0.242640687119285
x%5B2%5D+=+%28-%288%29-sqrt%28+72+%29%29%2F2%5C1+=+-8.24264068711928

Quadratic expression 1x%5E2%2B8x%2B-2 can be factored:
1x%5E2%2B8x%2B-2+=+%28x-0.242640687119285%29%2A%28x--8.24264068711928%29
Again, the answer is: 0.242640687119285, -8.24264068711928. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-2+%29