What is x^2-18x+14<0 ?

The solution to x^2-18x+14<0 is -sqrt(67)+9<x<sqrt(67)+9

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x^2-18x+14<0

x^{2} - 18 x + 14 < 0

- 67 + 9 < x < 67 + 9

Interval Notation

(- 67 + 9, 67 + 9)

Decimal Notation

0.81464 \dots < x < 17.18535 \dots

Solution steps

x^{2} - 18 x + 14 < 0

Complete the square

x^{2} - 18 x + 14 : (x - 9)^{2} - 67

(x - 9)^{2} - 67 < 0

Move

67

to the right side

(x - 9)^{2} < 67

For

u^{n} < a

, if

n

is even then

- 67 < x - 9 < 67

a < u < b

then

a < u and u < b

- 67 < x - 9 and x - 9 < 67

- 67 < x - 9 : x > - 67 + 9

x - 9 < 67 : x < 67 + 9

Combine the intervals

x > - 67 + 9 and x < 67 + 9

Merge Overlapping Intervals

- 67 + 9 < x < 67 + 9

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