The solution to x^2-6x<=-4 is -sqrt(5)+3<= x<= sqrt(5)+3

Popular >

x^2-6x<=-4

Solution

x^{2} - 6 x \leq - 4

- 5 + 3 \leq x \leq 5 + 3

Interval Notation

[- 5 + 3, 5 + 3]

Decimal Notation

0.76393 \dots \leq x \leq 5.23606 \dots

Solution steps

x^{2} - 6 x \leq - 4

Rewrite in standard form

x^{2} - 6 x + 4 \leq 0

Complete the square

x^{2} - 6 x + 4 : (x - 3)^{2} - 5

(x - 3)^{2} - 5 \leq 0

Move

5

to the right side

(x - 3)^{2} \leq 5

For

u^{n} \leq a

, if

n

is even then

- 5 \leq x - 3 \leq 5

a \leq u \leq b

then

a \leq u and u \leq b

- 5 \leq x - 3 and x - 3 \leq 5

- 5 \leq x - 3 : x \geq - 5 + 3

x - 3 \leq 5 : x \leq 5 + 3

Combine the intervals

x \geq - 5 + 3 and x \leq 5 + 3

Merge Overlapping Intervals

- 5 + 3 \leq x \leq 5 + 3

∣ 4 - 4 ∣ + ∣ 4 + 3 ∣ - ∣ 4 ∣ \geq 3

x^{2} - 2 \geq 0

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

\frac{x ^{- 8} y ^{6} z ^{9}}{x y ^{7} z ^{3}}

- \frac{1}{( \frac{1}{9} ) ^{\frac{3}{2}}}