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How do you complete the square for quadratic equations

I am having trouble trying to solve quadratic equations by completing the square. 


Please provide a few examples of what you are having trouble with.
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1 Answer

If you have a quadratic equation such as  ax2 + bx + c = 0 and you want to solve it by completing the square, you can by following the steps:
1.  subtract c (or add if c is negative) from each side of the equation giving:   ax2 + bx     = - c
2.  if a ≠ 1, then divide through by a.  If a = 1, then skip this step:   x2 + (b/a)x = - c/a
3.  the missing term needed to complete the square is based on the coefficient for the x term.  (b/a)
      3a.  take half of this term and square it.      (b/a)/2 ->  b/(2a) ... and now square it....  (b/(2a))2 
      3b.  this is the number to add to both sides of the equation.
                                                 x2 + (b/a)x + (b/(2a))2  = - c/a + (b/(2a))2
4.  once you factor the expression on the left you will have a perfect square  (x + b/2a)2 and on the right...the rest will reduce to some number.
5.  Celebrate your successful completion of the square!!