The solution to x^2-4x+2<0 is -sqrt(2)+2<x<sqrt(2)+2

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x^2-4x+2<0

Solution

x^{2} - 4 x + 2 < 0

- 2 + 2 < x < 2 + 2

Interval Notation

(- 2 + 2, 2 + 2)

Decimal Notation

0.58578 \dots < x < 3.41421 \dots

Solution steps

x^{2} - 4 x + 2 < 0

Complete the square

x^{2} - 4 x + 2 : (x - 2)^{2} - 2

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

Move

2

to the right side

(x - 2)^{2} < 2

For

u^{n} < a

, if

n

is even then

- 2 < x - 2 < 2

a < u < b

then

a < u and u < b

- 2 < x - 2 and x - 2 < 2

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

x - 2 < 2 : x < 2 + 2

Combine the intervals

x > - 2 + 2 and x < 2 + 2

Merge Overlapping Intervals

- 2 + 2 < x < 2 + 2

8^{(\frac{3}{2})}

2 (x + 5) = 2 x + 5

2 x^{2} - 41 = 0

x^{2} - 6 x + 9 - y^{2}

12 - (u + 7) < 3 (u - 1)