What is x^2-12x+3<0 ?

The solution to x^2-12x+3<0 is -sqrt(33)+6<x<sqrt(33)+6

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x^2-12x+3<0

x^{2} - 12 x + 3 < 0

- 33 + 6 < x < 33 + 6

Interval Notation

(- 33 + 6, 33 + 6)

Decimal Notation

0.25543 \dots < x < 11.74456 \dots

Solution steps

x^{2} - 12 x + 3 < 0

Complete the square

x^{2} - 12 x + 3 : (x - 6)^{2} - 33

(x - 6)^{2} - 33 < 0

Move

33

to the right side

(x - 6)^{2} < 33

For

u^{n} < a

, if

n

is even then

- 33 < x - 6 < 33

a < u < b

then

a < u and u < b

- 33 < x - 6 and x - 6 < 33

- 33 < x - 6 : x > - 33 + 6

x - 6 < 33 : x < 33 + 6

Combine the intervals

x > - 33 + 6 and x < 33 + 6

Merge Overlapping Intervals

- 33 + 6 < x < 33 + 6

0.85 x = 200

5 + (2 x + 3)^{2} - (3 x + 2) (x + 1)

\frac{5}{6} + \frac{1}{3} \cdot \frac{5}{8}

a^{2} + 2 a + 5 = 0

\frac{1}{2} \cdot 2