What is 2x^2-10x+10<0 ?

The solution to 2x^2-10x+10<0 is (-sqrt(5)+5)/2 <x<(sqrt(5)+5)/2

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2x^2-10x+10<0

2 x^{2} - 10 x + 10 < 0

\frac{- 5 + 5}{2} < x < \frac{5 + 5}{2}

Interval Notation

(\frac{- 5 + 5}{2}, \frac{5 + 5}{2})

Decimal Notation

1.38196 \dots < x < 3.61803 \dots

Solution steps

2 x^{2} - 10 x + 10 < 0

Rewrite in standard form

x^{2} - 5 x + 5 < 0

Complete the square

x^{2} - 5 x + 5 : (x - \frac{5}{2})^{2} - \frac{5}{4}

(x - \frac{5}{2})^{2} - \frac{5}{4} < 0

Move

\frac{5}{4}

to the right side

(x - \frac{5}{2})^{2} < \frac{5}{4}

For

u^{n} < a

, if

n

is even then

- \frac{5}{4} < x - \frac{5}{2} < \frac{5}{4}

a < u < b

then

a < u and u < b

- \frac{5}{4} < x - \frac{5}{2} and x - \frac{5}{2} < \frac{5}{4}

- \frac{5}{4} < x - \frac{5}{2} : x > \frac{- 5 + 5}{2}

x - \frac{5}{2} < \frac{5}{4} : x < \frac{5 + 5}{2}

Combine the intervals

x > \frac{- 5 + 5}{2} and x < \frac{5 + 5}{2}

Merge Overlapping Intervals

\frac{- 5 + 5}{2} < x < \frac{5 + 5}{2}

- 2 < x + 3 < 2

6^{2} + 9^{2} = c^{2}

\frac{1}{6} + \frac{1}{6}

x (x + 3) = 4

x^{2} = 2.5

What is 2x^2-10x+10<0 ?
The solution to 2x^2-10x+10<0 is (-sqrt(5)+5)/2 <x<(sqrt(5)+5)/2