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Bot GPT 3.5 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.