Solve the equation using formula. $2x^{2}\, +\, \displaystyle \frac{x\, -\, 1}{5}\, =\, 0$
- $x\, =\, \displaystyle \frac{-1\, \pm\, \sqrt{10}}{4}$
- $x\, =\, \displaystyle \frac{-1\, \pm\, \sqrt{41}}{20}$
- $x\, =\, \displaystyle \frac{1\, \pm\, \sqrt{41}}{20}$
- $x\, =\, \displaystyle \frac{1\, \pm\, \sqrt{10}}{4}$
Reveal answer
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B
Correct answer
Explanation
Multiply by 5: 10x^2 + x - 1 = 0. Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a, we get x = (-1 +/- sqrt(1 - 4(10)(-1))) / 20 = (-1 +/- sqrt(41)) / 20.
AI explanation
Multiply the entire equation by 5 to clear the fraction, resulting in 10x squared plus x minus 1 equals 0. Using the quadratic formula x equals the quantity (-b plus or minus the square root of (b squared minus 4ac)) divided by 2a, substitute a equals 10, b equals 1, and c equals -1. This evaluates to x equals (-1 plus or minus the square root of 41) divided by 20.