Question
Solve for x using, Quadratic equations, factoring or completing the square.
x^2+4x+3=0
x^2+4x+3=0
Answers
GPT-4o mini
To solve the quadratic equation \( x^2 + 4x + 3 = 0 \), we can factor the equation.
1. **Factoring**: We need to find two numbers that multiply to \( 3 \) (the constant term) and add to \( 4 \) (the coefficient of \( x \)).
The numbers \( 1 \) and \( 3 \) satisfy both conditions:
\[
1 \times 3 = 3 \quad \text{and} \quad 1 + 3 = 4
\]
2. **Writing the factors**: We can then factor the quadratic as:
\[
(x + 1)(x + 3) = 0
\]
3. **Setting each factor to zero**:
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]
4. **Solutions**: Thus, the solutions to the equation \( x^2 + 4x + 3 = 0 \) are:
\[
x = -1 \quad \text{and} \quad x = -3
\]
You can verify these solutions by substituting them back into the original equation.
So, the final answer is:
\[
x = -1 \quad \text{or} \quad x = -3
\]
1. **Factoring**: We need to find two numbers that multiply to \( 3 \) (the constant term) and add to \( 4 \) (the coefficient of \( x \)).
The numbers \( 1 \) and \( 3 \) satisfy both conditions:
\[
1 \times 3 = 3 \quad \text{and} \quad 1 + 3 = 4
\]
2. **Writing the factors**: We can then factor the quadratic as:
\[
(x + 1)(x + 3) = 0
\]
3. **Setting each factor to zero**:
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]
4. **Solutions**: Thus, the solutions to the equation \( x^2 + 4x + 3 = 0 \) are:
\[
x = -1 \quad \text{and} \quad x = -3
\]
You can verify these solutions by substituting them back into the original equation.
So, the final answer is:
\[
x = -1 \quad \text{or} \quad x = -3
\]