Solve the equation using formula. $6m^{2}\, -\, 4m\, =\, 3$
- $m\, =\, \displaystyle \frac{-2\, \pm\, \sqrt{22}}{6}$
- $m\, =\, \displaystyle \frac{-4\, \pm\, \sqrt{22}}{12}$
- $m\, =\, \displaystyle \frac{2\, \pm\, \sqrt{22}}{6}$
- $m\, =\, \displaystyle \frac{4\, \pm\, \sqrt{22}}{12}$
Reveal answer
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C
Correct answer
Explanation
6m^2 - 4m - 3 = 0. Using quadratic formula: m = [-b +/- sqrt(b^2 - 4ac)] / 2a = [4 +/- sqrt(16 - 4*6*(-3))] / 12 = [4 +/- sqrt(16 + 72)] / 12 = [4 +/- sqrt(88)] / 12 = [4 +/- 2*sqrt(22)] / 12 = (2 +/- sqrt(22)) / 6.
AI explanation
Rewrite the equation in standard form as 6m^2 - 4m - 3 = 0, where a = 6, b = -4, and c = -3. Using the quadratic formula, m = (-b ± √(b^2 - 4ac)) / (2a). Substituting the values gives m = (4 ± √((-4)^2 - 4(6)(-3))) / 12, which simplifies to m = (4 ± √(16 + 72)) / 12 = (4 ± √88) / 12. Dividing the numerator and denominator by 2 results in m = (2 ± √22) / 6.