SOLUTION: 7a2 + 8a + 2 = 0 I have done most of the problems and this is the last one can you help me please....

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 7a2 + 8a + 2 = 0 I have done most of the problems and this is the last one can you help me please....      Log On


   

Question 172163: 7a2 + 8a + 2 = 0 I have done most of the problems and this is the last one can you help me please....
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

7a%5E2%2B8a%2B2=0 Start with the given equation.


Notice we have a quadratic equation in the form of aa%5E2%2Bba%2Bc where a=7, b=8, and c=2


Let's use the quadratic formula to solve for a


a+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


a+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%287%29%282%29+%29%29%2F%282%287%29%29 Plug in a=7, b=8, and c=2


a+=+%28-8+%2B-+sqrt%28+64-4%287%29%282%29+%29%29%2F%282%287%29%29 Square 8 to get 64.


a+=+%28-8+%2B-+sqrt%28+64-56+%29%29%2F%282%287%29%29 Multiply 4%287%29%282%29 to get 56


a+=+%28-8+%2B-+sqrt%28+8+%29%29%2F%282%287%29%29 Subtract 56 from 64 to get 8


a+=+%28-8+%2B-+sqrt%28+8+%29%29%2F%2814%29 Multiply 2 and 7 to get 14.


a+=+%28-8+%2B-+2%2Asqrt%282%29%29%2F%2814%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


a+=+%28-8%2B2%2Asqrt%282%29%29%2F%2814%29 or a+=+%28-8-2%2Asqrt%282%29%29%2F%2814%29 Break up the expression.


a+=+%28-4%2Bsqrt%282%29%29%2F%287%29 or a+=+%28-4-sqrt%282%29%29%2F%287%29 Reduce


So the answers are a+=+%28-4%2Bsqrt%282%29%29%2F%287%29 or a+=+%28-4-sqrt%282%29%29%2F%287%29


which approximate to a=-0.369 or a=-0.773