To solve the quadratic equation, we must factorize the left side into two factors
[tex]x^2+13x+40=0[/tex]
We have to look for two numbers their product = 40, and their sum = 13
Since 8 x 5 = 40 and 8 + 5 = 13, then the factors will be
(x + 5) and (x + 8)
[tex]\begin{gathered} x^2+13x+40=(x+5)(x+8) \\ (x+5)(x+8)=0 \end{gathered}[/tex]
Now we will equate each factor by 0
[tex]\begin{gathered} x+5=0 \\ x+8=0 \end{gathered}[/tex]
Let us solve them to find the values of x
x + 5 = 0
Subtract 5 from both sides
[tex]\begin{gathered} x+5-5=0-5 \\ x=-5 \end{gathered}[/tex]
x + 8 = 0
Subtract 8 from both sides
[tex]\begin{gathered} x+8-8=0-8 \\ x=-8 \end{gathered}[/tex]
The solution of the equation is
x = -5 and x = -8
The answer is
x = -5 and x = -8
