Question
Answer
$$81.573264+0.3476644x-0.0147314(x-13)^2=81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}81.573264+0.3476644x-0.0147314(x-13)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}81.573264+0.3476644x-0.0147314(x^2-26x+169) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}81.573264+0x-(0x^2+0x+0) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}81+0x+0x^2+0x+0 \xlongequal{ } \\[1 em] & \xlongequal{ }81 \cancel{0x}0x^2 \cancel{0x}0 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}81\end{aligned} $$ | |
| ① | Find $ \left(x-13\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 13 }$. $$ \begin{aligned}\left(x-13\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 13 + \color{red}{13^2} = x^2-26x+169\end{aligned} $$ |
| ② | Multiply $ \color{blue}{0} $ by $ \left( x^2-26x+169\right) $ $$ \color{blue}{0} \cdot \left( x^2-26x+169\right) = 0x^20x0 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 0x^20x0 \right) = 0x^20x0 $$ |
| ④ | Combine like terms: $$ \color{blue}{81} \, \color{red}{ \cancel{0x}} \,0x^2 \, \color{red}{ \cancel{0x}} \, \color{blue}{0} = \color{blue}{81} $$ |
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