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x^2+2x-12<0

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x²+2x−12<0

Solution

−√13−1<x<√13−1

Interval Notation

(−√13−1, √13−1)

Decimal

−4.60555…<x<2.60555…

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Solution steps

One step at a time

x²+2x−12<0

Complete the square x²+2x−12: (x+1)²−13

(x+1)²−13<0

Move 13 to the right side

(x+1)²<13

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

−√13<x+1<√13

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

−√13<x+1 and x+1<√13

−√13<x+1 : x>−√13−1

x+1<√13 : x<√13−1

Combine the intervals

x>−√13−1 and x<√13−1

Merge Overlapping Intervals

−√13−1<x<√13−1

Number Line

−√13−1<x<√13−1

Quadratic Inequalities Examples

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

x^2+2x-12<0

Solution

Solution steps

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