How do you solve for x in the equation x^2 + 10x + 12?

To solve the quadratic equation x² + 10x + 12 = 0, we can use the factoring method.

First, we need to express the equation in standard form:

x² + 10x + 12 = 0

Next, we look for two numbers that multiply to the constant term (12) and add up to the coefficient of the x term (10). The numbers 2 and 6 satisfy these conditions since:

• 2 × 6 = 12
• 2 + 6 = 10

Now we can factor the quadratic equation:

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

To find the values of x, we can set each factor equal to zero:

• x + 2 = 0 ⟹ x = -2
• x + 6 = 0 ⟹ x = -6

Therefore, the solutions for the equation x² + 10x + 12 = 0 are x = -2 and x = -6.