Question
Answer
$$0.05(x-5)^3-0.5x+5=5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}0.05(x-5)^3-0.5x+5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0.05(x^3-15x^2+75x-125)-0.5x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0x^3+0x^2+0x+0-0x+5 \xlongequal{ } \\[1 em] & \xlongequal{ }0x^30x^2 \cancel{0x}0 \cancel{0x}+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5\end{aligned} $$ | |
| ① | Find $ \left(x-5\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 5 $. $$ \left(x-5\right)^3 = x^3-3 \cdot x^2 \cdot 5 + 3 \cdot x \cdot 5^2-5^3 = x^3-15x^2+75x-125 $$ |
| ② | Multiply $ \color{blue}{0} $ by $ \left( x^3-15x^2+75x-125\right) $ $$ \color{blue}{0} \cdot \left( x^3-15x^2+75x-125\right) = 0x^30x^20x0 $$ |
| ③ | Combine like terms: $$ 0x^30x^2 \, \color{blue}{ \cancel{0x}} \, \color{green}{0} \, \color{blue}{ \cancel{0x}} \,+ \color{green}{5} = \color{green}{5} $$ |
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