Solve the equation x^2 + x − 42 = 0 for x by FACTORING. Please show all of your work.
To solve the equation x^2 + x − 42 = 0 by factoring, we need to find two numbers that multiply to give -42 and add up to 1 (the coefficient of x).
Factors of -42: -1, 1, -2, 2, -3, 3, -6, 6, -7, 7, -14, 14, -21, 21, -42, 42
After trying different combinations, we find that -6 and 7 meet the criteria: -6 * 7 = -42 and -6 + 7 = 1.
Therefore, the equation can be factored as follows:
(x - 6)(x + 7) = 0
Setting each factor equal to zero:
x - 6 = 0 or x + 7 = 0
Solving for x:
x = 6 or x = -7
So the solution to the equation x^2 + x - 42 = 0 by factoring is x = 6 or x = -7.