To complete the square, how do you find the value that must be added to the expression to make a perfect square trinomial? What is the value? x2 + 2 5 x + ?

Question

Gustavo

Mathematics

3 November, 00:45

To complete the square, how do you find the value that must be added to the expression to make a perfect square trinomial? What is the value? x2 + 2 5 x + ?

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Pamela Glass · Answer 1

Assume we ha a²+b², What value should be added to make a perfect square.

We know that (a+b) ² = a²+2ab+b², so we have to find 2ab. In the example

x²+25+?, the 2ab is missing, we know that the first term is x & te 2nd term is 5, then what is missing is twice the 1st term by the second in our case it will be

2 (1) (5) = 10, If we add 10, we will get x²+5²+10 that is (x+5) ². To keep the equation as it is do subtract 10 (since we added 10 to get the perfect square.

Hence the equation become (x+5) ² - 10