What is (x-6)^2<sqrt(10)(x-6) ?

The solution to (x-6)^2<sqrt(10)(x-6) is -sqrt(5/2)-(-12-sqrt(10))/2 <x<sqrt(5/2)-(-12-sqrt(10))/2

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(x-6)^2<sqrt(10)(x-6)

(x - 6)^{2} < 10 (x - 6)

- \frac{5}{2} - \frac{- 12 - 10}{2} < x < \frac{5}{2} - \frac{- 12 - 10}{2}

Interval Notation

(- \frac{5}{2} - \frac{- 12 - 10}{2}, \frac{5}{2} - \frac{- 12 - 10}{2})

Decimal Notation

6 < x < 9.16227 \dots

Solution steps

(x - 6)^{2} < 10 (x - 6)

Rewrite in standard form

x^{2} - 12 x + 36 + 610 - 10 x < 0

Complete the square

x^{2} - 12 x + 36 + 610 - 10 x : (x + \frac{- 12 - 10}{2})^{2} - \frac{77}{2} + 36

(x + \frac{- 12 - 10}{2})^{2} - \frac{77}{2} + 36 < 0

Identify the intervals

- \frac{5}{2} - \frac{- 12 - 10}{2} < x < \frac{5}{2} - \frac{- 12 - 10}{2}

\frac{2}{3} y - \frac{2}{5} = 5

(- 1)^{10}

- 3 x - 3 (- 5 x - 17) = 3

4 (x + 4) = 52

\frac{1}{- 4.9 9 ^{2} - 25}

What is (x-6)^2<sqrt(10)(x-6) ?
The solution to (x-6)^2<sqrt(10)(x-6) is -sqrt(5/2)-(-12-sqrt(10))/2 <x<sqrt(5/2)-(-12-sqrt(10))/2