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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?

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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?

Jan 26, 2018
edited by Guest  Jan 26, 2018

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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?

$$\begin{array}{|lrcll|} \hline &(9x^2+10x+c) &=& (3x+b)^2 \\ & &=& 9x^2+\underbrace{6b}_{=10}x+\underbrace{b^2}_{=c} \\\\ \hline (1) & 6b &=& 10 \\ & b &=& \frac53 \\\\ (2) & c &=& b^2 \\ & c &=& (\frac53)^2 \\ & c &=& \frac{25}{9} \\ \hline &\left(9x^2+10x+\dfrac{25}{9} \right) &=& \left(3x+\dfrac53 \right)^2 \\ \hline \end{array}$$

Jan 26, 2018