SOLUTION: {{{y^2 + 8y = 2}}} I have tried this problem a number of times and i never get the right combination let alone the right numbers. The answers available are: a) -8.2,0.2 b)8.2,-0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: {{{y^2 + 8y = 2}}} I have tried this problem a number of times and i never get the right combination let alone the right numbers. The answers available are: a) -8.2,0.2 b)8.2,-0      Log On


   

Question 37633: y%5E2+%2B+8y+=+2 I have tried this problem a number of times and i never get the right combination let alone the right numbers. The answers available are: a) -8.2,0.2 b)8.2,-0.2 c)0.3,7.7 d)-7.7,-0.3. The only numbers I get are 0.2, 0.3, and 0.4, which is not one of the numbers. Please help!
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2+%2B+8y+=+2
y%5E2+%2B+8y+-+2+=+0
Use quadratic fomula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-8+%2B-+sqrt%28+%288%29%5E2-4%2A%281%29%2A%28-2%29+%29%29%2F%282%2A%281%29%29+
x+=+%28-8+%2B-+sqrt%28+64+%2B+8+%29%29%2F%282%29+
x+=+%28-8+%2B-+sqrt%28+72+%29%29%2F%282%29+
x+=+%28-8+%2B-+sqrt%28+72+%29%29%2F%282%29+
x+=+%28-8+%2B-+6%2Asqrt%28+2+%29%29%2F%282%29+
x+=+%28-4+%2B-+3%2Asqrt%28+2+%29%29+
Answer is B
Solved by pluggable solver: SOLVE quadratic equation with variable
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+=+1%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