Question

Solve the following quadratic by factoring.

t²-6t-16=0
List the answers separated by a comma. For example, if you found solutions t=1 and t=2 , you would enter 1, 2. Provide your answer below

Answer 1

To solve the quadratic equation t² - 6t - 16 = 0 by factoring, find two numbers whose product is the constant term (-16) and whose sum is the coefficient of the middle term (-6). The equation can be factored as (t - 8)(t + 2) = 0. The solutions are t = 8 and t = -2.

Step-by-step explanation:

To solve the quadratic equation t² - 6t - 16 = 0 by factoring, we need to find two numbers whose product is the constant term (-16) and whose sum is the coefficient of the middle term (-6). The numbers that satisfy these conditions are -8 and 2, as -8 * 2 = -16 and -8 + 2 = -6. Therefore, the equation can be factored as (t - 8)(t + 2) = 0. Setting each factor equal to zero, we find the solutions t = 8 and t = -2. So, the answers are 8, -2.