We are given that the cost of manufacturing "x" units is given by the following formula:
[tex]C(x)=x^2+10x+60[/tex]
We are asked to determine the number of units "x" for a cost C = $13260. To do that we will replace the value of "C" in the equation for 13260:
[tex]13260=x^2+10x+60[/tex]
Now we subtract 13260 from both sides, we get:
[tex]\begin{gathered} 13260-13260=x^2+10x+60-13260 \\ 0=x^2+10x-13200 \end{gathered}[/tex]
Now, to solve this equation we will factor the equation. To do that we re write the factors as this:
[tex](x\cdot\cdot)(x\cdot\cdot)=0[/tex]
Now we need to determine two numbers which product ios -13260 and which algebraic sum is 10, those numbers are 120 and -110, since:
[tex]\begin{gathered} 120\times(-110)=-13260 \\ 120-110=10 \end{gathered}[/tex]
Replacing the number we get:
[tex](x+120)(x-110)=0[/tex]
Now we set each factor to zero and solve for "x":
[tex]\begin{gathered} x+120=0 \\ x=-120 \\ \end{gathered}[/tex]
The second factor is:
[tex]\begin{gathered} x-110=0 \\ x=110 \end{gathered}[/tex]
Since the number of units should be a positive number we get that the number of units must be 110.
