Solve the following equation by grouping
`x^{2}+5x+6=0`
Put your answer in the answer box below.
To solve the equation `x^2 + 5x + 6 = 0` by grouping, we need to find two numbers that multiply to 6 and add up to 5 (the coefficient of the middle term).
The numbers that satisfy these conditions are 2 and 3.
Now, we can split the middle term 5x into two terms using these numbers: `x^2 + 2x + 3x + 6 = 0`.
Next, we can factor by grouping:
(x^2 + 2x) + (3x + 6) = 0
x(x + 2) + 3(x + 2) = 0
Now, we have a common factor of (x + 2):
(x + 2)(x + 3) = 0
Finally, we set each factor equal to zero and solve for x:
x + 2 = 0 => x = -2
x + 3 = 0 => x = -3
So, the solutions to the equation are x = -2 and x = -3.