solve x2 + x - 6 = 0 by factoring

Answer 1

To solve x^2 + x - 6 = 0 by factoring, we need to find two numbers that multiply to -6 and add up to 1, the coefficient of the x term.

The two numbers that satisfy these conditions are 3 and -2, because 3 * -2 = -6 and 3 + (-2) = 1.

Therefore, we can rewrite the equation as:

x^2 + 3x - 2x - 6 = 0

Now, we can factor by grouping:

x(x + 3) - 2(x + 3) = 0

(x - 2)(x + 3) = 0

Setting each factor to zero, we get:

x - 2 = 0 or x + 3 = 0

Solving for x, we find:

x = 2 or x = -3

Therefore, the solutions to the equation x^2 + x - 6 = 0 are x = 2 and x = -3.