To solve the quadratic equation x² + 4x – 12 = 0, we can use the factoring method or the quadratic formula. Let’s first try factoring.
We need to find two numbers that multiply to -12 (the constant term) and add up to 4 (the coefficient of the x term). These numbers are 6 and -2, because:
6 * (-2) = -12
6 + (-2) = 4
Now we can rewrite the equation as:
(x + 6)(x – 2) = 0
Next, we set each factor equal to zero:
x + 6 = 0 or x – 2 = 0
Solving these gives:
x = -6 or x = 2
So the solutions to the equation x² + 4x – 12 = 0 are x = -6 and x = 2.
In summary, to solve this quadratic equation, we factored it, found the roots, and the solutions are x = -6 and x = 2.