How do you complete the square?

Say you start with a general equation of x2+ax+b=0. (If the x2 has a coefficient the you will need to divide by that first.)

You need to move to the equation (x+a/2)2 -(a/2)2+b=0. Then put all of the constants together on the other side and square root everything so you end up with x-a/2 equalling plus or minus the square root of (a/2)2-b. You can then move to x equalling a/2 plus or minus the square root of (a/2)2-b.

For example, x2+6x+2=0 --> (x+3)2-32+2 =0 --> (x+3)2 =7 --> x+3 =+/-sqrt(7) --> x=-3+/-sqrt(7)

Answered by Bryony C. Maths tutor

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