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Completing the Square

Completing the Square 1.2 - Solution

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We want to find the value of that would make the left-hand side of the equation a perfect square trinomial. Remember that the first and third terms must be perfect squares. Also, if and are the first and third terms, the middle term must be the product of and For the given equation, we will rewrite the first and third terms as perfect squares.
Now, the middle term must be the product of and
Therefore, if we assume we have that Let's rewrite the expression by substituting for and show that it is a perfect square trinomial.
We found that if the left-hand side of the equation is a perfect square trinomial. What would happen if Let's see.
If the left-hand side of the equation is also a perfect square trinomial. Thus, there are two possible values for that make a perfect square trinomial: and