The solution to (x+3)^2<2 is -sqrt(2)-3<x<sqrt(2)-3

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(x+3)^2<2

Solution

(x + 3)^{2} < 2

- 2 - 3 < x < 2 - 3

Interval Notation

(- 2 - 3, 2 - 3)

Decimal Notation

- 4.41421 \dots < x < - 1.58578 \dots

Solution steps

(x + 3)^{2} < 2

For

u^{n} < a

, if

n

is even then

- 2 < x + 3 < 2

a < u < b

then

a < u and u < b

- 2 < x + 3 and x + 3 < 2

- 2 < x + 3 : x > - 2 - 3

x + 3 < 2 : x < 2 - 3

Combine the intervals

x > - 2 - 3 and x < 2 - 3

Merge Overlapping Intervals

- 2 - 3 < x < 2 - 3

[b + 6] + 6 = - 7

\frac{1}{3 + 2 i}

\frac{2 n - 8}{n ^{2} - 16}

12 x - 5 = 9 x^{2}

6 x + 29 + 3 x + 124 = 180