Solve the equation x2+x − 42 = 0 for x by FACTORING.

Question

Please show all of your work.

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Answer 1

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.