Posted by **lisa** on Thursday, November 2, 2006 at 11:19pm.

it is called completing the square

here is the equation 4x^2-4x+1=9 if anyone can help me please do okay i really need ot understand this

4x^2-4x+1=9

**Move the numbers to the other side.
**

4x^2 -4x = 9-1

4x^2 -4x = 8

Now factor out 4 to make things easier.

x^2 -x =2 but remember we have all of that multiplied by 4.

The completed square goes where I place the Y.

x^2 - x +Y = 2 and to keep everything equal we must add Y to the right side, also.

x^2 - x + Y = 2 + Y

To determine what number completes the square, take 1/2 the x term and square it. 1/2 of 1 is 1/2 and 1/2 squared is 1/4. Now add 1/4 to both sides like this.

x^2 - x + 1/4 = 2 + 1/4 = 2.25

Now factor the left side. It is a perfect square now so it will be

(x - 1/2)^2 = 2.25

Now take the square root of both sides and solve for x. I hope this helps.

solving polynomial long division
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