Final answer:
The quadratic equation 6x²+11x-2=0 can be solved using the quadratic formula. The solutions are x = 1/6 and x = -2.
Step-by-step explanation:
The student is asking to solve a quadratic equation of the form ax²+bx+c = 0. Specifically, the equation given is 6x²+11x-2=0. To solve this, we can use the quadratic formula, which is x = (-b ± √(b²-4ac)) / (2a). In this case, a = 6, b = 11, and c = -2. Using the quadratic formula with these values entered, we obtain:
x = [-(11) ± √((11)²-4(6)(-2))] / (2(6))
x = [-11 ± √(121+48)] / 12
x = [-11 ± √(169)] / 12
x = [-11 ± 13] / 12
So, the two possible solutions for x are:
- x = (13 - 11) / 12 = 2/12 = 1/6
- x = (-11 - 13) / 12 = -24/12 = -2
Therefore, the solutions to the equation 6x²+11x-2=0 are x = 1/6 and x = -2.