Question

Derive quadratic formula by completing square method

Answer 1

Answer:

Complete the Square

ax2 + bx + c has "x" in it twice, which is hard to solve.

But there is a way to rearrange it so that "x" only appears once. It is called Completing the Square (please read that first!).

Our aim is to get something like x2 + 2dx + d2, which can then be simplified to (x+d)2

So, let's go:

Start with ax^2 + bx + c=0

Divide the equation by a x^2 + bx/a + c/a = 0

Put c/a on other side x^2 + bx/a = -c/a

Add (b/2a)2 to both sides x^2 + bx/a + (b/2a)^2 = -c/a + (b/2a)^2

The left hand side is now in the x2 + 2dx + d2 format, where "d" is "b/2a"

So we can re-write it this way:

"Complete the Square" (x+b/2a)^2 = -c/a + (b/2a)^2