SOLUTION: The problem asks to solve by whatever method seems easiest to you. I have tried so many methods and can't seem to figure these two out. (a) x^2+8x=-16 (b) 3x^2=2x+5 Thank you fo

Algebra ->  Equations -> SOLUTION: The problem asks to solve by whatever method seems easiest to you. I have tried so many methods and can't seem to figure these two out. (a) x^2+8x=-16 (b) 3x^2=2x+5 Thank you fo      Log On


   

Question 320286: The problem asks to solve by whatever method seems easiest to you. I have tried so many methods and can't seem to figure these two out. (a) x^2+8x=-16 (b) 3x^2=2x+5
Thank you for your time =)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(a) x^2+8x=-16 (b) 3x^2=2x+5
----------------------
x^2+8x+16 = 0
3x^2- 2x -5 = 0
3x^2+24x+48 = 0
---------------- Subtract
-26x - 53 = 0
x = -53/26
------------- That's not right
x^2 + 8x + 16 = 0
4x^2- 8x - 20 = 0
-------------------Add
5x^2 = 4
x = ± 2sqrt(5)/5
------------- That's not right either
x^2+8x+16 = 3x^2- 2x -5
2x^2 - 10x - 21 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-10x%2B-21+=+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=%28-10%29%5E2-4%2A2%2A-21=268.

Discriminant d=268 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+268+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+268+%29%29%2F2%5C2+=+6.59267638593623
x%5B2%5D+=+%28-%28-10%29-sqrt%28+268+%29%29%2F2%5C2+=+-1.59267638593623

Quadratic expression 2x%5E2%2B-10x%2B-21 can be factored:
2x%5E2%2B-10x%2B-21+=+%28x-6.59267638593623%29%2A%28x--1.59267638593623%29
Again, the answer is: 6.59267638593623, -1.59267638593623. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-10%2Ax%2B-21+%29

------------------
That's right.