Solve the following equation by grouping. x2+10x+21=0 .
Show your work.
(2 points)
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.