Solve the following equation by grouping. x2+10x+21=0 .
Show your work.
(2 points)
To solve the equation by grouping, we need to find two numbers that multiply to give 21 and add up to give 10.
The factors of 21 are 1, 21, 3, and 7.
The pair that adds up to 10 is 3 and 7.
Now, we can rewrite the middle term of the equation as the sum of 3x and 7x:
x^2 + 3x + 7x + 21 = 0
Next, we group the terms:
(x^2 + 3x) + (7x + 21) = 0
Now, we can factor out the greatest common factor from each group:
x(x + 3) + 7(x + 3) = 0
Notice that we now have a common factor of (x + 3), so we can combine the two groups:
(x + 3)(x + 7) = 0
Finally, we can set each factor equal to zero and solve for x:
x + 3 = 0 --> x = -3
x + 7 = 0 --> x = -7
Therefore, the solutions to the equation are x = -3 and x = -7.