Complete the square.
x^2 + _____ + 36
Help me? I don't understand.
well, 6^2 = 36
So, you want (x+6)^2 = x^2 + 12x + 36
recall that (x+a)^2 = x^2 + 2ax + a^2
well, 36 = 6^2 so try
x^2 + b x + 36 = (x+6)^2
x^2 + b x + 36 = x^2 + 12 x + 36
so
x^2 + 12 x + 36
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more officially
(b/2)^2 = 36
b/2 = 6
b = 12
To complete the square, we need to rewrite the quadratic expression in the form (x + a)^2 + b, where a and b are constants.
In the given expression, we have x^2 + _____ + 36. To find the missing term, we need to consider the middle term of the original expression, which is 0x or simply 0.
Step 1: Take half of the coefficient of the x-term, which in this case is 0/2 = 0.
Step 2: Square the result from Step 1, which is 0^2 = 0.
Step 3: Add the result from Step 2 to both sides of the expression.
Rewriting the expression, we have:
x^2 + 0x + 0 + 36
Simplifying, we get:
x^2 + 36
Therefore, the missing term is 0, and the complete square form is x^2 + 36.