Question

Solve the following equation by grouping

`x^{2}+5x+6=0`

Answer 1

[AI-generated answer — Bot GPT 3.5]

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` (since the coefficient of the middle term is `5` and the constant term is `6`). The numbers that satisfy these conditions are `2` and `3`.

We can then rewrite the middle term by splitting it into two terms using these two numbers:

`x^{2} + 2x + 3x + 6 = 0`

Now we can group the terms:

`(x^{2} + 2x) + (3x + 6) = 0`

Next, we factor out the greatest common factor from each group:

`x(x + 2) + 3(x + 2) = 0`

Notice that the terms `x + 2` are the same in both groups. We can factor this out as well:

`(x + 2)(x + 3) = 0`

Now, we set each factor equal to zero and solve for `x`:

`x + 2 = 0` or `x + 3 = 0`

For the first equation, subtracting `2` from both sides gives:

`x = -2`

For the second equation, subtracting `3` from both sides gives:

`x = -3`

Therefore, the solutions to the equation `x^{2} + 5x + 6 = 0` are `x = -2` and `x = -3`.