Question
solve the following equations.
x^2+3x+2x+6=0
x^2+3x+2x+6=0
Answers
Answered by
GPT-4o mini
To solve the equation \(x^2 + 3x + 2x + 6 = 0\), we first simplify the equation:
\[
x^2 + (3x + 2x) + 6 = 0
\]
This simplifies to:
\[
x^2 + 5x + 6 = 0
\]
Next, we can factor the quadratic equation. We are looking for two numbers that multiply to \(6\) (the constant term) and add to \(5\) (the coefficient of \(x\)). These numbers are \(2\) and \(3\).
So, we can factor the equation as:
\[
(x + 2)(x + 3) = 0
\]
Setting each factor equal to zero gives us the solutions:
1. \(x + 2 = 0 \implies x = -2\)
2. \(x + 3 = 0 \implies x = -3\)
Thus, the solutions to the equation \(x^2 + 5x + 6 = 0\) are:
\[
\boxed{-2} \quad \text{and} \quad \boxed{-3}
\]
\[
x^2 + (3x + 2x) + 6 = 0
\]
This simplifies to:
\[
x^2 + 5x + 6 = 0
\]
Next, we can factor the quadratic equation. We are looking for two numbers that multiply to \(6\) (the constant term) and add to \(5\) (the coefficient of \(x\)). These numbers are \(2\) and \(3\).
So, we can factor the equation as:
\[
(x + 2)(x + 3) = 0
\]
Setting each factor equal to zero gives us the solutions:
1. \(x + 2 = 0 \implies x = -2\)
2. \(x + 3 = 0 \implies x = -3\)
Thus, the solutions to the equation \(x^2 + 5x + 6 = 0\) are:
\[
\boxed{-2} \quad \text{and} \quad \boxed{-3}
\]