## anonymous 5 years ago How do you complete a square for example: y=x^2-6x+4

1. nowhereman

Find the numbers a and b so that the x^2 and x part of (ax + b)^2 and your polynomial are the same. Then add the difference in the part without x, to get equality.

2. anonymous

you lost me

3. anonymous

so is a 1 b 6?

4. amistre64

when you "complete the square", you end up with: -b/2a +- sqrt(b^2 -4ac)/2a completeing the square is just the proof of the quadratic formula

5. anonymous

Ok so no calc expierence just algebra

6. amistre64

in your example: a = 1 , b=-6 , c=4

7. amistre64

just algebra :)

8. anonymous

in order to get the answer do I do the wuadratic formula?

9. amistre64

When we square a value for "x", we get a quadratic equation; the name quadratic is a fancy latin word meaning: we squared it and got a result.

10. amistre64

11. amistre64

(x+3)^2 = x^2 +6x +9 right? but if we have the equation: x^2 + 6x +6 we need to convert it to a "complete" square so that we can factor it.....

12. amistre64

in fact, we just need to add 9 and subtract 9 to the equation to make it still equal the same amuont right? +9-9 = 0 and 0 added to any number doesnt change the value.

13. anonymous

hold on ok so I just got the answer for x thru the quadratic formula now what do I do?

$x ^{2}-6x+4=y$ Take half of the coefficient of x, in this case half of the -6 giving you a -3. Square this and add it your equation$x ^{2}-6x +(-3)^{2}+4=y +(-3)^{2}$ $x ^{2}-6x+9 =y-4-9=y-13$ $(x-3)^{2}=y-13$$x-3=\pm \sqrt{y-13}$

15. amistre64

x^2 + 6x +6 x^2 +6x +9 -9 +6 (x^2 +6x +9) -3 ^^^^^^^^^ this part here is now a "completed square" (x+3)^2 - 3

16. amistre64

$x=3\pm \sqrt{y-13}$

18. amistre64

radar did a fine job at that...great job :)

Time I finished typing it was answered LOL

20. amistre64

lol....at least its there for the rest of posterity to read ;)