To solve the quadratic equation x² + 5x + 6 = 0, we can factor the equation or use the quadratic formula. In this case, factoring is straightforward.
First, we look for two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of x). The numbers 2 and 3 fit this requirement since:
- 2 * 3 = 6
- 2 + 3 = 5
We can therefore factor the equation as:
(x + 2)(x + 3) = 0
Next, we set each factor equal to zero:
- x + 2 = 0 ⇒ x = -2
- x + 3 = 0 ⇒ x = -3
Thus, the solutions to the equation x² + 5x + 6 = 0 are:
- x = -2
- x = -3
This means the quadratic intersects the x-axis at these two points, which is helpful for graphing the equation or understanding its roots.