x2+x − 42 = 0

for x by FACTORING.

1 answer

To factor the given equation x^2 + x - 42 = 0, we need to find two numbers that multiply to -42 and add up to 1.

To do this, we can list all the factor pairs of 42:
1, 42
2, 21
3, 14
6, 7

Among these pairs, the pair 6 and 7 has a sum of 13. Since we need the sum of the factors to be 1, we need to use the negative values of 6 and 7.

Therefore, we can rewrite the equation as:
(x + 7)(x - 6) = 0

Setting each factor equal to zero, we have:
x + 7 = 0 or x - 6 = 0
x = -7 or x = 6

So the solutions to the equation x^2 + x - 42 = 0 are x = -7 and x = 6.