Question

Solve the following quadratic by factoring.

a²-4a-12=0
List the answers separated by a comma. For example, if you found solutions a=1 and a=2 , you would enter 1, 2.
190

Answer 1

The quadratic equation a²-4a-12=0 is factored into (a - 6)(a + 2) = 0. By setting each factor equal to zero, we find that the solutions are a = 6 and a = -2.

Step-by-step explanation:

To solve the quadratic equation a²-4a-12=0 by factoring, we need to find two numbers that multiply to -12 (the constant term) and add up to -4 (the coefficient of the a term).

The numbers that satisfy these conditions are -6 and +2 because (-6)*(+2) = -12 and (-6)+(+2) = -4.

Next, we can factor the equation as follows:

• Write the equation with two binomials: (a - 6)(a + 2) = 0
• Set each factor equal to zero to find the solutions for a: a - 6 = 0 or a + 2 = 0
• Solve each equation: a = 6 or a = -2

Therefore, the solutions to the quadratic equation are a = 6 and a = -2.