SOLUTION: Solve the following quadratic equation by using completing the square. 1.) 4x²-x-8=0 2.) x²+5x-3=0 3.) 8y²-24y-3=0

Algebra ->  Equations -> SOLUTION: Solve the following quadratic equation by using completing the square. 1.) 4x²-x-8=0 2.) x²+5x-3=0 3.) 8y²-24y-3=0      Log On


   

Question 1166286: Solve the following quadratic equation by using completing the square.
1.) 4x²-x-8=0
2.) x²+5x-3=0
3.) 8y²-24y-3=0
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!



1)  +4x%5E2-x-8+=+0+



Divide both sides by 4:

     +x%5E2-%281%2F4%29x-2+=+0+



Add 2 both sides:

      +x%5E2+-+%281%2F4%29x+=+2+

  

Add +%28%281%2F2%29%281%2F4%29%29%5E2+=+1%2F64+ to both sides:

      +x%5E2+-%281%2F4%29x+%2B+1%2F64+=+2+%2B+1%2F64+



Simplify RHS: 

    +x%5E2+-%281%2F4%29x+%2B+1%2F64+=+129%2F64+



Notice LHS is perfect square:

    +%28x-1%2F8%29%5E2+=+129%2F64+ 



Take sqrt both sides, use +/- on RHS (b/c LHS^2 = RHS^2 we otherwise would lose the negative solution):

     ++%28x-1%2F8%29+ = +- +sqrt%28129%2F64%29+



Add 1/8 to both sides:

     ++x+=+%281%2F8%29+%2B-+sqrt%28129%2F64%29+



This can be written:

     +x+=+%281+%2B-+sqrt%28129%29%29%2F8+



Note that there are two solutions, agreeing with the highest power of the polynomial (2).







The others are procedurally the same.