Question 219583: X^2 + 12X
i am suppose to determin the constant that should be added to the binomial so that it becomes a perfect square trinomial. Found 2 solutions by Alan3354, jsmallt9:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! X^2 + 12X
i am suppose to determin the constant that should be added to the binomial so that it becomes a perfect square trinomial.
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If the coefficient a of the x^2 term = 1, then add
(b/2)^2.
b = 12
(b/2)^2 = 36
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x^2 + 12x + 36 = (x+6)^2
Since you have +12x we'll match your expression to the first one. Perfect square trinomials start with a perfect square term and, fortunately, your expression starts with a perfect square term: . Whatever expression is being squared in this term is our "a" in the pattern. So our "a" is "x".
Perfect square trinomials also end in a perfect square term. (This is what you are trying to figure out.) Whatever is being squared in the last term is your "b".
The middle term must fit the pattern "2ab" where "a" is whatever is being squared in the front and "b" is whatever is being squared at the end. So we want your "12x" to fit the "2ab" pattern. In other words we want 12x = 2ab. Since we know that our "a" is "x", this becomes 12x = 2(x)(b). Dividing both sides by 2x we get: 6 = b.
Now that we know what "b" is and since the last term, the one we are looking for, is supposed to be , we want the last term to be .
So adding 36 to will make it a perfect square trinomial.
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