Question

Solve the following equation by grouping. x2+10x+21=0 .

Show your work.

(2 points)

Answer 1

To solve the equation by grouping, we are looking for two numbers whose sum is 10 and whose product is 21.

Factors of 21 are: 1, 3, 7 and 21.

Among these factors, 3 and 7 sum up to 10, so we can rewrite the middle term of the equation as 3x + 7x.

x^2 + 3x + 7x + 21 = 0

Now we can group the terms:

(x^2 + 3x) + (7x + 21) = 0

Factor out the greatest common factor from each group:

x(x + 3) + 7(x + 3) = 0

Now we can see that both groups have a common factor of (x + 3), so we can factor that out:

(x + 3)(x + 7) = 0

Now we have a product that equals zero, so we can set each factor equal to zero:

x + 3 = 0 or x + 7 = 0

Solving these equations gives us:

x = -3 or x = -7

Therefore, the solutions to the equation x^2 + 10x + 21 = 0 are x = -3 and x = -7.