Solve the equation x2+x − 42 = 0 for x by FACTORING.
Please show all of your work.
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To solve the equation x^2 + x - 42 = 0 by factoring, we need to find two numbers whose product is -42 and whose sum is 1 (the coefficient of x).
The prime factorization of 42 is 2 * 3 * 7.
After trying different pairs of factors, we find that -6 and 7 satisfy the conditions.
Therefore, we can rewrite the equation as:
(x - 6)(x + 7) = 0.
Now, we can set each factor equal to zero and solve for x:
x - 6 = 0 or x + 7 = 0
Solving the first equation, we get:
x = 6
Solving the second equation, we get:
x = -7
So the solutions to the equation x^2 + x - 42 = 0 by factoring are:
x = 6 or x = -7.