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.

Answer 1

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.