If you have a quadratic equation such as ax^{2} + 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: ax^{2} + bx = - c

2. if a ≠ 1, then divide through by a. If a = 1, then skip this step: x^{2} + (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.

x^{2} + (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!!

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