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

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x^2<= 4x-2

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

Solution

x^{2} \leq 4 x - 2

- 2 + 2 \leq x \leq 2 + 2

Interval Notation

[- 2 + 2, 2 + 2]

Decimal Notation

0.58578 \dots \leq x \leq 3.41421 \dots

Solution steps

x^{2} \leq 4 x - 2

Rewrite in standard form

x^{2} + 2 - 4 x \leq 0

Complete the square

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

(x - 2)^{2} - 2 \leq 0

Move

2

to the right side

(x - 2)^{2} \leq 2

For

u^{n} \leq a

, if

n

is even then

- 2 \leq x - 2 \leq 2

a \leq u \leq b

then

a \leq u and u \leq b

- 2 \leq x - 2 and x - 2 \leq 2

- 2 \leq x - 2 : x \geq - 2 + 2

x - 2 \leq 2 : x \leq 2 + 2

Combine the intervals

x \geq - 2 + 2 and x \leq 2 + 2

Merge Overlapping Intervals

- 2 + 2 \leq x \leq 2 + 2

3 x^{2} + 9 x - 54

∣ 4 x - 2 ∣ \geq 3 x + 1

x^{6} - 2 x^{3} + 1

\frac{( 5 - i )}{( 4 + 3 i )}

18 + 32