SOLUTION: Can someone please show the steps for this question . please and thanks Use mx^2 + nx+o and write the proof of the quadratic equation using m,n,o

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone please show the steps for this question . please and thanks Use mx^2 + nx+o and write the proof of the quadratic equation using m,n,o       Log On


   



Question 713018: Can someone please show the steps for this question . please and thanks


Use mx^2 + nx+o and write the proof of the quadratic equation using m,n,o

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

mx%5E2+%2B+nx+%2B+o+=+0

mx%5E2+%2B+nx+=+-o%0D%0A%0D%0A%7B%7B%7Bexpr%28m%2Fm%29x%5E2+%2B+expr%28n%2Fm%29x+=+-o%2Fm


x%5E2+%2B+expr%28n%2Fm%29x+=+-o%2Fm

Complete the square:

1. Multiply expr%28n%2Fm%29 by 1%2F2:

    expr%28n%2Fm%29%2Aexpr%281%2F2%29
    n%2F%282m%29

2. Square that result:

    %28n%2F%282m%29%29%5E2
     
    n%5E2%2F%282%5E2m%5E2%29

    n%5E2%2F%284m%5E2%29

3. Add to both sides of x%5E2+%2B+expr%28n%2Fm%29x+=+-o%2Fm

x%5E2+%2B+expr%28n%2Fm%29x+%2B+n%5E2%2F%284m%5E2%29+=+-o%2Fm+%2B+n%5E2%2F%284m%5E2%29 

Factor the left side;  Get LCD of 4m%5E2 on the right
and multiply the first term on the right by %284m%29%2F%284m%29



%28x+%2B+n%5E2%2F%282m%29%29%5E2+=+%28-4mo%29%2F%284m%5E2%29+%2B+n%5E2%2F%284m%5E2%29

%28x+%2B+n%5E2%2F%282m%29%29%5E2+=+%28-4mo%2B+n%5E2%29%2F%284m%5E2%29

Use the principle of square roots:

x+%2B+n%5E2%2F%282m%29+=++%22%22+%2B-+sqrt%28+%28-4mo%2B+n%5E2%29%2F%284m%5E2%29%29

x+%2B+n%2F%282m%29+=++%22%22+%2B-+sqrt%28+-4mo%2B+n%5E2%29%2Fsqrt%284m%5E2%29

 x+%2B+n%2F%282m%29+=++%22%22+%2B-+sqrt%28+-4mo%2B+n%5E2%29%2F%282m%29

    +x+=+-+n%2F%282m%29+%2B-+sqrt%28+-4mo%2B+n%5E2%29%2F%282m%29

    x+=+%28-n+%2B-+sqrt%28+-4mo%2Bn%5E2+%29%29%2F%282m%29+ 

    x+=+%28-n+%2B-+sqrt%28n%5E2-4mo+%29%29%2F%282m%29+
Edwin