Question
Answer
$$0.636(x-4.991)^2+11.66-((-0.9(x+2.55))^3+3.81)=8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}0.636(x-4.991)^2+11.66-((-0.9(x+2.55))^3+3.81)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0.636(x^2-8x+16)+11.66-((-0.9(x+2.55))^3+3.81) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0x^2+0x+0+11.66-((-(0x+0))^3+3.81) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}11-((-(0x+0))^3+3.81) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}11-((0x+0)^3+3.81) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}11-(0x^3+0x^2+0x+0+3.81) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}11-3 \xlongequal{ } \\[1 em] & \xlongequal{ }8\end{aligned} $$ | |
| ① | Find $ \left(x-4\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}{ 4 }$. $$ \begin{aligned}\left(x-4\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 4 + \color{red}{4^2} = x^2-8x+16\end{aligned} $$ |
| ② | Multiply $ \color{blue}{0} $ by $ \left( x^2-8x+16\right) $ $$ \color{blue}{0} \cdot \left( x^2-8x+16\right) = 0x^20x0 $$Multiply $ \color{blue}{0} $ by $ \left( x+2\right) $ $$ \color{blue}{0} \cdot \left( x+2\right) = 0x0 $$ |
| ③ | Combine like terms: $$ 0x^20x \color{blue}{0} + \color{blue}{11} = \color{blue}{11} $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left(0x0 \right) = 0x0 $$ |
| ⑤ | Find $ \left(0x+0\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 0x $ and $ B = 0 $. $$ \left(0x+0\right)^3 = \left( 0x \right)^3+3 \cdot \left( 0x \right)^2 \cdot 0 + 3 \cdot 0x \cdot 0^2+0^3 = 0x^30x^20x0 $$ |
| ⑥ | Combine like terms: $$ 0x^30x^20x \color{blue}{0} + \color{blue}{3} = \color{blue}{3} $$ |
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