Question

Solve: 5m²-m-6=0. Multiple answers, if any, should be separated by a comma. Enter only integer (s) or fraction (s).

Answer 1

To solve the equation 5m² - m - 6 = 0, you can use factoring. The solutions to the equation are m = 6/5 or m = -1.

Step-by-step explanation:

To solve the equation 5m² - m - 6 = 0, we can use factoring or the quadratic formula. Let's use factoring.

1. First, multiply the coefficient of the leading term (5) with the constant term (-6) to get -30.
2. Find two numbers that multiply to -30 and add up to the coefficient of the middle term (-1) which are -6 and 5.
3. Split the middle term using these numbers: 5m² - 6m + 5m - 6 = 0.
4. Factor by grouping: (5m² - 6m) + (5m - 6) = 0.
5. Factor out the GCF from each group: m(5m - 6) + 1(5m - 6) = 0.
6. Now, factor out the common binomial: (5m - 6)(m + 1) = 0.
7. Set each factor equal to zero and solve for m: 5m - 6 = 0 or m + 1 = 0.
8. Solve each equation: m = 6/5 or m = -1.

So, the solutions to the equation 5m² - m - 6 = 0 are m = 6/5 or m = -1.