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

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2(x-3)^2<3

Solution

2 (x - 3)^{2} < 3

- \frac{3}{2} + 3 < x < \frac{3}{2} + 3

Interval Notation

(- \frac{3}{2} + 3, \frac{3}{2} + 3)

Decimal Notation

1.77525 \dots < x < 4.22474 \dots

Solution steps

2 (x - 3)^{2} < 3

Divide both sides by

2

(x - 3)^{2} < \frac{3}{2}

For

u^{n} < a

, if

n

is even then

- \frac{3}{2} < x - 3 < \frac{3}{2}

a < u < b

then

a < u and u < b

- \frac{3}{2} < x - 3 and x - 3 < \frac{3}{2}

- \frac{3}{2} < x - 3 : x > - \frac{3}{2} + 3

x - 3 < \frac{3}{2} : x < \frac{3}{2} + 3

Combine the intervals

x > - \frac{3}{2} + 3 and x < \frac{3}{2} + 3

Merge Overlapping Intervals

- \frac{3}{2} + 3 < x < \frac{3}{2} + 3

x^{2} - 6 x + 9 = 11

10 x^{2} - 80

x - 3 x + 9 = 4 - 5 x + 2

\frac{n}{80} = \frac{35}{100}

x^{2} + 16 x = - 39