What is 13x^2+2x>= 2 ?

The solution to 13x^2+2x>= 2 is x = (3sqrt(3)-1)/(13)

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13x^2+2x>= 2

13 x^{2} + 2 x \geq 2

x \leq \frac{- 3 3 - 1}{13} or x \geq \frac{3 3 - 1}{13}

Interval Notation

(- \infty, \frac{- 3 3 - 1}{13}] \cup [\frac{3 3 - 1}{13}, \infty)

Decimal Notation

x \leq - 0.47662 \dots or x \geq 0.32278 \dots

Solution steps

13 x^{2} + 2 x \geq 2

Rewrite in standard form

13 x^{2} + 2 x - 2 \geq 0

Complete the square

13 x^{2} + 2 x - 2 : 13 (x + \frac{1}{13})^{2} - \frac{27}{13}

13 (x + \frac{1}{13})^{2} - \frac{27}{13} \geq 0

Move

\frac{27}{13}

to the right side

13 (x + \frac{1}{13})^{2} \geq \frac{27}{13}

Divide both sides by

13

(x + \frac{1}{13})^{2} \geq \frac{27}{169}

For

u^{n} \geq a

, if

n

is even then

x + \frac{1}{13} \leq - \frac{27}{169} or x + \frac{1}{13} \geq \frac{27}{169}

x + \frac{1}{13} \leq - \frac{27}{169} : x \leq \frac{- 3 3 - 1}{13}

x + \frac{1}{13} \geq \frac{27}{169} : x \geq \frac{3 3 - 1}{13}

Combine the intervals

x \leq \frac{- 3 3 - 1}{13} or x \geq \frac{3 3 - 1}{13}

\frac{n}{n ^{- 5}}

(x + 10) (x - 5) = (x + 1)^{2}

∣ 2 x - 5 ∣ = 6

Y = 0 - 5

\frac{2 ( \frac{8}{15} )}{1 - ( \frac{8}{15} ) ^{2}}

What is 13x^2+2x>= 2 ?
The solution to 13x^2+2x>= 2 is x<= (-3sqrt(3)-1)/(13)\lor x>= (3sqrt(3)-1)/(13)