Answer:
To put this equation in standard form, you need to complete the square for both the x's and the y's.
First, complete the square for the x's by adding and subtracting (16/2)^2 = 16^2/2^2 = 32/2 = 16.
4x² - 16x + 16 - 16 - 5y² - 30y - 9 = 0
4x² - 16x + 16 - 5y² - 30y - 9 = 0
Now, complete the square for the y's by adding and subtracting (30/2)^2 = 30^2/2^2 = 900/2 = 450.
4x² - 16x + 16 - 5y² - 30y + 450 - 450 - 9 = 0
4x² - 16x + 16 - 5(y² - 15y + 225) - 9 = 0
Now, you can simplify the expression inside the parentheses by completing the square for y.
4x² - 16x + 16 - 5(y - 15)^2 + 5*225 - 9 = 0
Now, divide everything by -5 to get the equation in standard form:
-4/5x² + 16/5x - 16/5 - (y - 15)^2 = 0
The standard form of the equation is:
(-4/5)x² + (16/5)x - 16/5 - (y - 15)^2 = 0