# Math Help - Complete the Square

1. ## Complete the Square

1. x^2 + 2x + k
2. kx^2 + 2x + k
3. x^2 - 3kx + 1

For the first I get: -1+- root(1+k)
Second : [-1+- root(1-k)]/k

But I'm told im wrong. Help!

2. are you supposed to just find k? or solve for k?

x² + 2x + k
x² + 2x + 1 + k - 1
(x + 1)² + k -1

not sure if that is what you mean

since there is no equation, there is nothing to solve

hope that helps maybe?

3. solve for x,

4. Originally Posted by phgao
1. x^2 + 2x + k
2. kx^2 + 2x + k
3. x^2 - 3kx + 1

For the first I get: -1+- root(1+k)
Second : [-1+- root(1-k)]/k

But I'm told im wrong. Help!
Hello,

the title of your message suggests, that you are looking for a value of k so you got a square. Is this right? If so:

to 1) $k=1 \ \mbox{then you get} \ (x+1)^2$
to 2) $k=1 \ \mbox{then you get} \ (x+1)^2$
to 3) $k=\frac{2}{3} \ \mbox{then you get} \ (x-1)^2$

I hope that this here is of some help.

Bye

5. Originally Posted by phgao
1. x^2 + 2x + k
2. kx^2 + 2x + k
3. x^2 - 3kx + 1

For the first I get: -1+- root(1+k)
Second : [-1+- root(1-k)]/k

But I'm told im wrong. Help!
"Complete the square" means complete the perfect square. Perfect square here is in the form (x+a)^2, where "a" is plus or minus, depending on the given data.

Before attempting completing the square, make sure first that the coeff(icient of the x^2 is 1 only. Meaning, it it were originally b(x^2), then divide it by "b"......

Completing the square of (x^2 +bx) is adding, and subtracting at the same time, the square of half of the coefficient of linear x.
x^2 +bx +(b/2)^2 -(b/2)^2 ------------***

------------------------
x^2 +2x +k = 0
x^2 +2x +(2/2)^2 -(2/2)^2 +k = 0
x^2 +2x +1 -1 +k = 0
(x+1)^2 -1 +k = 0
(x+1)^2 = 1-k
Take the square roots of both sides,
x+1 = +,-sqrt(1-k)
So,

----------------------
kx^2 +2x +k = 0

The x^2 has a coefficient k which is not 1, so divide kx^2 by k. In so doing, divide also all of the other terms of the original equation by k to retain the equality of the original equation.
x^2 +(2/k)x +1 = 0
Now that the coefficient of the x^2 is 1 only, we can start completing the square,
x^2 +(2/k)x +(1/k)^2 -(1/k)^2 +1 = 0
(x +1/k)^2 -1/(k^2) +1 = 0
(x +1/k)^2 = 1/(k^2) -1
x +1/k = +,-sqrt[1/(k^2) -1]
x = -1/k +,-sqrt[1/(k^2) -1] ------------answer.

--------------------------------
x^2 -3kx +1 = 0
x^2 -3kx +(-3k/2)^2 -(-3k/2)^2 +1 = 0
(x -3k/2)^2 -(9/4)k^2 +1 = 0
(x -3k/2)^2 = (9/4)k^2 -1
x -3k/2 = +,-sqrt[(9/4)k^2 -1]
x = 3k/2 +,-sqrt[(9/4)k^2 -1] ----------answer.