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The quadratic $x^2-20x+36$ can be written in the form $(x+b)^2+c$, where $b$ and $c$ are constants. What is $b+c$?

 May 6, 2018
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The quadratic $x^2-20x+36$ can be written in the form $(x+b)^2+c$, where $b$ and $c$ are constants.

What is $b+c$?

 

\(\begin{array}{|rclrcl|} \hline x^2+20x+36 &=& (x+b)^2+c \\ &=& x^2+\underbrace{2b}_{=20}\cdot x + \underbrace{(b^2+c)}_{=36} \\ \hline 2b &=& 20 & b^2+c &=& 36 \\ \mathbf{b} &\mathbf{=}& \mathbf{10} & 10^2+c &=& 36 \\ &&& c &=& 36 - 100 \\ &&& \mathbf{c} &\mathbf{=}& \mathbf{-64} \\\\ b+c &=& 10-64 \\ \mathbf{b+c} &\mathbf{=}& \mathbf{-54}\\ \hline \end{array}\)

 

laugh

 May 7, 2018

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