Question

Complete the square.
Can you show how please, I'm lost
X^2 + 20x - 4y + 100 = 0

Answer 1

ignore -4y for now, put of to side

so what you do

(x^2+20x+100)-4y=0
take 1/2 of 20 and squaer it to get 100
neat, 100 is already there
so then factor perefect square
(x+10)²-4y=0
that is how you complete the square
if we had 4y² instead of 4y we could get
(x+10-2y)(x+10+2y)=0 but we don't


completed square is
(x+10)²-4y=0

Answer 2

Ignore the -4y term for now. Only focus on x^2+20x+100. This can be factored to (x+10)^2. Notice how expanding it out gives

(x+10)^2 = (x+10)(x+10)
(x+10)^2 = x(x+10) + 10(x+10)
(x+10)^2 = x^2+10x + 10x + 100
(x+10)^2 = x^2 + 20x + 100

So this means
x^2+20x-4y+100 = 0
turns into
(x+10)^2 - 4y = 0
after we factor

The second equation listed above implies that we have a parabola because we can solve for y to get
-4y = -(x+10)^2
y = (1/4)(x+10)^2