Solve the quadratic equation 3x2+x−14=03𝑥2+𝑥−14=0 using the quadratic formula. Please show all your work with the Quad Formula to earn your points.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
For the equation 3x^2 + x - 14 = 0, we have a = 3, b = 1, and c = -14.
Substitute these values into the formula:
x = (-(1) ± √((1)^2 - 4(3)(-14))) / 2(3)
x = (-1 ± √(1 + 168)) / 6
x = (-1 ± √169) / 6
x = (-1 ± 13) / 6
This gives two possible solutions:
x = (-1 + 13) / 6 = 12 / 6 = 2
x = (-1 - 13) / 6 = -14 / 6 = -7/3
Therefore, the solutions to the quadratic equation 3x^2 + x - 14 = 0 are x = 2 and x = -7/3.