Solve the equation by factoring. Show all of your work to receive full credit. x2+4x − 12=0 (2 points)

Answer 1

To solve the equation by factoring, we need to find two numbers whose sum is 4 and whose product is -12.

Let's write the equation in the form:

x^2 + 4x - 12 = 0

Now, let's factor the equation.

We need to find two numbers that multiply to give -12 and add up to 4. After some trial and error, we can find that the numbers are 6 and -2.

So, we can write the equation as:

(x + 6)(x - 2) = 0

Now, we can set each factor equal to zero:

x + 6 = 0 or x - 2 = 0

To solve for x, we can subtract 6 from both sides in the first equation, and add 2 to both sides in the second equation:

x = -6 or x = 2

So, the solutions to the equation x^2 + 4x - 12 = 0 are x = -6 and x = 2.