Completing the square?

Question

Write the following equation in the correct form.

x^2-4x+10y=0

 

The answer is y − 2/5 = − 1/10 (x − 2)2 but I do not understand why?

 

how would you complete the square?

 

Answer 1

x² - 4x + 10y = 0

x² - 4x = -10y

x² - 4x + 4 = -10y + 4

(x - 2)² = -10y + 4

(-1/10)(x - 2)² = y - 2/5

Answer 2

When you complete the square, you take 1/2 of the coefficient of the x term, square it, and add it to both sides of the equation, or expressing this algebraically:

 

Given ax² + bx + c = 0, take (b/2)² and add to both sides

 

We have x² - 4x + 10y = 0

 

x² - 4x = -10y   (We take 1/2 of -4, which is -2, and square it. (-2)² = 4. Now, add 4 to both sides)

 

x² - 4x + 4 = -10y + 4

 

(x - 2)² = -10 (y - 2/5)

 

-1/10 (x - 2)² = y - 2/5