5x^3-2=x-x^2

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

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^□√☐

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log_□

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ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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5x³−2=x−x²

Solution

x≈ 0.75863…

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Solution steps

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5x³−2=x−x²

Move x² to the left side

5x³−2+x²=x

Move x to the left side

5x³−2+x²−x=0

Write in the standard form a_nxⁿ+… +a₁x+a₀=0

5x³+x²−x−2=0

Find one solution for 5x³+x²−x−2=0 using Newton-Raphson: x≈ 0.75863…

Apply long division: 5x³+x²−x−2x−0.75863… =5x²+4.79319…x+2.63630…

5x²+4.79319…x+2.63630…≈ 0

Find one solution for 5x²+4.79319…x+2.63630…=0 using Newton-Raphson: No Solution for x∈ℝ

The solution is

x≈ 0.75863…

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

5x^3-2=x-x^2

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