How do you complete the square for quadratic equations

Question

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

Answer 1

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!!