Answer:
[tex]x = -1, -3[/tex]
Solve by Factoring
To solve by factoring, we will split up the equation using our factoring rules.
In this particular instance, we will factor out common variables.
We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.
[tex]x^2 + 4x + 3 = 0[/tex]
[tex](x+3)(x+1)=0[/tex]
Set each factor equal to zero and solve.
Root 1
[tex]x+3=0[/tex]
[tex]x=-3[/tex]
Root 2
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
The final answer is [tex]\boxed{x = -1, -3}[/tex].
As requested in the question, we must now check with the quadratic formula.
What is the quadratic formula?
To solve this quadratic equation, we will utilize the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].
We will define our variables:
Now, we will plug these into the equation and solve the equation.
Solve
[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]
Root 1
[tex]\displaystyle x=\frac{-4+2}{2}[/tex]
[tex]\displaystyle x=\frac{-2}{2}[/tex]
[tex]\boxed{x=-1}[/tex]
Root 2
[tex]\displaystyle x=\frac{-4-2}{2}[/tex]
[tex]\displaystyle x=\frac{-6}{2}[/tex]
[tex]\boxed{x=-3}[/tex]
Final Answer
The final answer is [tex]\boxed{x = -1, -3}[/tex].
To learn more about the quadratic formula, visit this question:
https://brainly.com/question/19630217
