1-x-x^2>0

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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

simplify solve for inverse tangent line

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1−x−x²>0

Solution

−√5−12 <x<√5−12

Interval Notation

(−√5−12 , √5−12 )

Decimal

−1.61803…<x<0.61803…

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Solution steps

One step at a time

1−x−x²>0

Complete the square 1−x−x²: −(x+12 )²+54

−(x+12 )²+54 >0

Move 54 to the right side

−(x+12 )²>−54

Multiply both sides by −1

(x+12 )²<54

For uⁿ < a, if n is even then −ⁿ√a < u < ⁿ√a

−√54 <x+12 <√54

If a<u<b then a<u and u<b

−√54 <x+12 and x+12 <√54

−√54 <x+12 : x>−√5−12

x+12 <√54 : x<√5−12

Combine the intervals

x>−√5−12 and x<√5−12

Merge Overlapping Intervals

−√5−12 <x<√5−12

Number Line

−√5−12 <x<√5−12

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

1-x-x^2>0

Solution

Solution steps

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