what number is used to complete the square for the equation y^2 + 16 = -y?
a).-25
b).25
c)-64
d)64
a
no i meant b
What does it take in the ___ space to make
y^2 + y + __ a perfect square?
Think of the general expression
ay^2 + by + c.
When a = 1, square half the "b" term to get the c that makes it a perfect square (y + b/2)^2 = y^2 + by + b^2/4
You need to learn to do this yourself.
Yes, 1/4 is the answer
thanks drwls
To complete the square for the equation y^2 + 16 = -y, we want to rearrange the equation so that it is in the form (y + a)^2 = b, where 'a' is a number that completes the square and 'b' is the constant term.
First, we move the -y term to the left side of the equation by adding 'y' to both sides:
y^2 + y + 16 = 0
To complete the square, we will add a term and its square to both sides of the equation. The term we add is half the coefficient of 'y', which is (1/2)(1) = 1/2. And, we square this term, which gives us (1/2)^2 = 1/4.
Adding 1/4 to both sides of the equation, we get:
y^2 + y + 1/4 + 16 = 1/4
Now, let's simplify the equation:
(y + 1/2)^2 + 16 = 1/4
To isolate the perfect square term on the left side, we subtract 16 from both sides of the equation:
(y + 1/2)^2 = 1/4 - 16
Simplifying the right side:
(y + 1/2)^2 = 1/4 - 64/4
(y + 1/2)^2 = -63/4
From the equation (y + a)^2 = b, we can see that 'a' is 1/2 and 'b' is -63/4.
None of the given answer choices matches -63/4, so none of them is correct for completing the square in this equation. Hence, there is no correct answer among the options provided (a, b, c, and d).