What is x^2<= 8x-13 ?

The solution to x^2<= 8x-13 is -sqrt(3)+4<= x<= sqrt(3)+4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2<= 8x-13

x^{2} \leq 8 x - 13

- 3 + 4 \leq x \leq 3 + 4

Interval Notation

[- 3 + 4, 3 + 4]

Decimal Notation

2.26794 \dots \leq x \leq 5.73205 \dots

Solution steps

x^{2} \leq 8 x - 13

Rewrite in standard form

x^{2} + 13 - 8 x \leq 0

Complete the square

x^{2} + 13 - 8 x : (x - 4)^{2} - 3

(x - 4)^{2} - 3 \leq 0

Move

3

to the right side

(x - 4)^{2} \leq 3

For

u^{n} \leq a

, if

n

is even then

- 3 \leq x - 4 \leq 3

a \leq u \leq b

then

a \leq u and u \leq b

- 3 \leq x - 4 and x - 4 \leq 3

- 3 \leq x - 4 : x \geq - 3 + 4

x - 4 \leq 3 : x \leq 3 + 4

Combine the intervals

x \geq - 3 + 4 and x \leq 3 + 4

Merge Overlapping Intervals

- 3 + 4 \leq x \leq 3 + 4

- 2 d \geq 26

\frac{8 + 3 i}{5 - 2 i}

2 x - 59 = 3 x - 77

\frac{1}{3} - 9

41.1 = 4 x^{2}