Respuesta :
Answer:
[tex]c=1[/tex] and [tex]c=-12[/tex]
Step-by-step explanation:
The correct equation is:
[tex]c^2+11c=12[/tex]
To solve by completing the square method.
Solution:
We have:
[tex]c^2+11c=12[/tex]
In order to solve by completing the square method we will carry out the following operations to the given equation to get a perfect square binomial.
We can write as:
[tex]c^2+2.\frac{11}{2}c=12[/tex]
[tex]c^2+2.\frac{11}{2}c+(\frac{11}{2})^2-(\frac{11}{2})^2=12[/tex]
[tex](c+\frac{11}{2})^2-(\frac{11}{2})^2=12[/tex] [As [tex]c^2+2.\frac{11}{2}c+(\frac{11}{2})^2=(c+\frac{11}{2})^2[/tex]]
Adding both sides by [tex](\frac{11}{2})^2[/tex]
[tex](c+\frac{11}{2})^2-(\frac{11}{2})^2+(\frac{11}{2})^2=12+(\frac{11}{2})^2[/tex]
[tex](c+\frac{11}{2})^2=12+\frac{121}{4}[/tex]
Taking LCD to add fraction.
[tex](c+\frac{11}{2})^2=\frac{48}{4}+\frac{121}{4}[/tex]
[tex](c+\frac{11}{2})^2=\frac{169}{4}[/tex]
Taking square root both sides.
[tex]\sqrt{(c+\frac{11}{2})^2}=\sqrt{\frac{169}{4}}[/tex]
[tex]c+\frac{11}{2}=\pm\frac{13}{2}[/tex]
Subtracting both sides by [tex]\frac{11}{2}[/tex] :
[tex]c+\frac{11}{2}-\frac{11}{2}=\pm\frac{13}{2}-\frac{11}{2}[/tex]
[tex]c=\pm\frac{13}{2}-\frac{11}{2}[/tex]
So, we have:
[tex]c=\frac{13}{2}-\frac{11}{2}[/tex] and [tex]c=-\frac{13}{2}-\frac{11}{2}[/tex]
[tex]c=\frac{2}{2}[/tex] and [tex]c=\frac{-24}{2}[/tex]
[tex]c=1[/tex] and [tex]c=-12[/tex] (Answer)
