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scoundrel [369]
3 years ago
6

When completing the square on the equation c2 + 110 = 12, the resulting solution is: It

Mathematics
1 answer:
Delvig [45]3 years ago
6 0

Answer:

c=1 and c=-12

Step-by-step explanation:

The correct equation is:

c^2+11c=12

To solve by completing the square method.

Solution:

We have:

c^2+11c=12

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:

c^2+2.\frac{11}{2}c=12  

c^2+2.\frac{11}{2}c+(\frac{11}{2})^2-(\frac{11}{2})^2=12

(c+\frac{11}{2})^2-(\frac{11}{2})^2=12  [As  c^2+2.\frac{11}{2}c+(\frac{11}{2})^2=(c+\frac{11}{2})^2]

Adding both sides by (\frac{11}{2})^2

(c+\frac{11}{2})^2-(\frac{11}{2})^2+(\frac{11}{2})^2=12+(\frac{11}{2})^2

(c+\frac{11}{2})^2=12+\frac{121}{4}  

Taking LCD to add fraction.

(c+\frac{11}{2})^2=\frac{48}{4}+\frac{121}{4}

(c+\frac{11}{2})^2=\frac{169}{4}

Taking square root both sides.

\sqrt{(c+\frac{11}{2})^2}=\sqrt{\frac{169}{4}}

c+\frac{11}{2}=\pm\frac{13}{2}

Subtracting both sides by \frac{11}{2} :

c+\frac{11}{2}-\frac{11}{2}=\pm\frac{13}{2}-\frac{11}{2}

c=\pm\frac{13}{2}-\frac{11}{2}

So, we have:

c=\frac{13}{2}-\frac{11}{2} and c=-\frac{13}{2}-\frac{11}{2}

c=\frac{2}{2} and c=\frac{-24}{2}

c=1 and c=-12  (Answer)

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