Complete the square?

Question

x2-6x=12
x2-12x=-4
y2+14y=0

Answer 1

x^2-6x=12
x^2-6x + 9 = 12 + 9
(x - 3)^2 = 21

(x-3) = +/- sqrt (21)
x = 3 +/- sqrt (21)

x^2-12x=-4
x^2-12x + (12/2)^2=-4 + (12/2)^2
x^2-12x +36 = -4 + 36
(x - 6)^2 = 32
(x - 6) = +/- sqrt(16 * 2)
x = 6 +/- 4sqrt (2)

y^2+14y=0
y^2+14y + 7^2=0 + 7^2
(y + 7)^2 = 49
(y + 7) = +/- sqrt(49)
y + 7 = +/- 7
y = 7 +/- 7

y = 7 + 7 = 14
y = 7 - 7 = 0

Answer 2

It is much better if YOU complete the square. Since the coefficient of the quadratic term is 1, the procedure is not too hard. Let me show you 1, then you can do others.
x2 - 6x -12 = 0 (added -12 to both sides)
The perfect square (x+b)^2 = x2 + 2b x + b2
So you look at the "x-term" and figure out what b is. In this case, it is -3. Now find out what b2 is; in this case +9. We'll, I don't have +9 there, but I can "fake" it by replacing -12 with (-21 + 9). So now the problem has become
x2 - 6x + 9 - 21 = 0
we can add 21 to both sides to isolate the square and we have (x - 3)^2 = 21
Take square roots, x-3 = +/- sqrt(21).
So the solutions will be x = 3+ sqrt(21) and
x= 3-sqrt(21).

Answer 3

completing the square is done by dividing the x^1 term by two, and then squaring the result. You then then add that number to both sides of the original equation. Example:

x^2 - 6x = 12

6/2 = -3
3^2 = 9

x^2 - 6x + 9 = 12 +9

(x -3)^2 = 21

Answer 4

Hi,

First Problem:

x ^ 2 - 6y + 9 = 21

(x - 3) ^ 2 = 21

Second Problem:

x ^ 2 - 12x + 36 = 32

(x - 6) ^ 2 = 32

Third Problem:

y^2 + 14y + 49 = 49

(y + 7)^2 = 49

I hope that helps! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 5

(x-3)2=21
(x-6)2=32
(y+7)2=49