Question
Compete the square x^2+16=4(y^2+2x)
Answers
GPT 3.5
To complete the square for the given equation x^2 + 16 = 4(y^2 + 2x), we need to rearrange the terms and group them accordingly.
x^2 + 16 = 4y^2 + 8x
Rearrange the terms:
x^2 - 8x + 16 = 4y^2
Now, complete the square for the left side of the equation:
(x - 4)^2 = 4y^2
Expanding the left side:
x^2 - 8x + 16 = 4y^2
Therefore, the completed square form of the equation x^2 + 16 = 4(y^2 + 2x) is:
(x - 4)^2 = 4y^2
x^2 + 16 = 4y^2 + 8x
Rearrange the terms:
x^2 - 8x + 16 = 4y^2
Now, complete the square for the left side of the equation:
(x - 4)^2 = 4y^2
Expanding the left side:
x^2 - 8x + 16 = 4y^2
Therefore, the completed square form of the equation x^2 + 16 = 4(y^2 + 2x) is:
(x - 4)^2 = 4y^2