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If c is a constant such that 9x^2+10x+c is equal to the square of a binomial, then what is c?

 Mar 14, 2020
 #1
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Completing the square, we get (3x + 5/6)^2, so c = 25/36.

 Mar 14, 2020
 #2
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Since the first term of  9x2 + 10x + c  is  9, in factored form it must look like:  (3x + a)2.

Expanding  (3x + a)2  =  9x2 + 6ax + a2

This means that  10x = 6ax   --->   6a  =  10   --->   a  =  10/6   --->   a  =  5/3

Placing this value of  a  into  (3x + a)   --->   (3x + 5/3)2   --->   9x2 + 10x + 25/9

So:  c = 25/9.

 Mar 14, 2020

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