How can I solve quadratic equations by completing the square?
When we have a quadratic (ax2 + bx + c = 0) we can "complete the square" to solve for x. For example x2 + 8x + 7 = 0. First look at the x2 + 8x, in particular the coefficient of x, "b", which in this case is 8. Halve this number and put into a bracket with x, which will be squared (x + 4)2 . If we were to expand this we would get x2 + 8x good so far + 16 not what we need. To equate our expressions then, we need to subtract 16 from (x + 4)2. Rewriting our original equation with x2 + 8x substituted by (x + 4)2 -16, gives us (x + 4)2 -16 + 7 = 0, which rearranges to give (x + 4)2 - 9 = 0. Some basic algebra lets us now solve this: (x + 4)2 = 9; (x + 4) = 3 or -3; x = -1 and -7. When dealing with quadratics where "a" is not 1, we must first divide by "a" to get the term x2. Completing the square is a very useful tool to solve quadratics when it is not doable by sight, as well as for finding minimum values.
