Final answer:
To find the values of k that will cause the equation to have 2 real solutions, we need to use the discriminant of the quadratic equation. The values of k that satisfy the inequality k < 3/2 will give the equation two real solutions.
Step-by-step explanation:
To find the values of k that will cause the equation to have 2 real solutions, we need to use the discriminant of the quadratic equation. The discriminant is given by the formula b² - 4ac, where a, b, and c are the coefficients of the quadratic equation. In this case, we have a = 6, b = 6, and c = k. The equation will have 2 real solutions if the discriminant is greater than 0, meaning b² - 4ac > 0. Substituting the values, we get: 6² - 4(6)(k) > 0. Simplifying this inequality gives us 36 - 24k > 0. To solve for k, we isolate the variable: k < 36/24, which simplifies to k < 3/2. Therefore, the values of k that will cause the equation to have 2 real solutions are any values less than 3/2.