SOLUTION: Find two numbers whose difference is 8 and the sum of the square of the smaller number and twice the square of the larger number is 363. I need help setting it up and solving i

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Find two numbers whose difference is 8 and the sum of the square of the smaller number and twice the square of the larger number is 363. I need help setting it up and solving i      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 907795: Find two numbers whose difference is 8 and the sum of the square of the smaller number and twice the square of the larger number is 363.
I need help setting it up and solving it
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x the smaller umber
x^2 + 2(x+8)^2 = 363
2x^2 + 32x + 128 = 363
2x^2 + 32x - 235 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B32x%2B-235+=+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=%2832%29%5E2-4%2A2%2A-235=2904.

Discriminant d=2904 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+2904+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+2904+%29%29%2F2%5C2+=+5.47219358530748
x%5B2%5D+=+%28-%2832%29-sqrt%28+2904+%29%29%2F2%5C2+=+-21.4721935853075

Quadratic expression 2x%5E2%2B32x%2B-235 can be factored:
2x%5E2%2B32x%2B-235+=+2%28x-5.47219358530748%29%2A%28x--21.4721935853075%29
Again, the answer is: 5.47219358530748, -21.4721935853075. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B32%2Ax%2B-235+%29