The solution to 5x^2+x-1<0 is (-sqrt(21)-1)/(10)<x<(sqrt(21)-1)/(10)

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5x^2+x-1<0

Solution

5 x^{2} + x - 1 < 0

\frac{- 21 - 1}{10} < x < \frac{21 - 1}{10}

Interval Notation

(\frac{- 21 - 1}{10}, \frac{21 - 1}{10})

Decimal Notation

- 0.55825 \dots < x < 0.35825 \dots

Solution steps

5 x^{2} + x - 1 < 0

Complete the square

5 x^{2} + x - 1 : 5 (x + \frac{1}{10})^{2} - \frac{21}{20}

5 (x + \frac{1}{10})^{2} - \frac{21}{20} < 0

Move

\frac{21}{20}

to the right side

5 (x + \frac{1}{10})^{2} < \frac{21}{20}

Divide both sides by

5

(x + \frac{1}{10})^{2} < \frac{21}{100}

For

u^{n} < a

, if

n

is even then

- \frac{21}{100} < x + \frac{1}{10} < \frac{21}{100}

a < u < b

then

a < u and u < b

- \frac{21}{100} < x + \frac{1}{10} and x + \frac{1}{10} < \frac{21}{100}

- \frac{21}{100} < x + \frac{1}{10} : x > \frac{- 21 - 1}{10}

x + \frac{1}{10} < \frac{21}{100} : x < \frac{21 - 1}{10}

Combine the intervals

x > \frac{- 21 - 1}{10} and x < \frac{21 - 1}{10}

Merge Overlapping Intervals

\frac{- 21 - 1}{10} < x < \frac{21 - 1}{10}

- \frac{\frac{51}{52}}{- \frac{17}{26}}

7 - 3 (2) = 3 + c (2)

\frac{3 m}{2 m + 1} + \frac{11 m + 7}{2 m + 1}

2 x^{2} - 2 x - 24

∣ x - 3 ∣ = 7

What is 5x^2+x-1<0 ?
The solution to 5x^2+x-1<0 is (-sqrt(21)-1)/(10)<x<(sqrt(21)-1)/(10)