Question 632953: Complete the trinomial so it is a perfect square. x^2 + ___+ 64
Thanks a lot! Found 2 solutions by Edwin McCravy, MathTherapy:Answer by Edwin McCravy(20055) (Show Source):
x² + ___ + 64
We know it must end up as the square of the sum of the square roots of
the given first and third terms. The square root of x² is x and the
square root of 64 is 8. We multiply out the square of their sum, which
is (x+8)²:
(x+8)² = (x+8)(x+8) = x² + 8x + 8x + 64 = x² + 16x + 64.
So we see now that the middle term has to be the same as that middle term,
which is 16x:
x² + 16x + 64
You can do that or you can memorize the rule. The middle term is always
TWICE THE PRODUCT OF THE TWO SQUARE ROOTS.
The two square roots are x and 8. Their product is 8x and twice that is 16x.
The first way is when you can't remember the rule.
Edwin
