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