Chapter 12.5, Problem 10MRE

To determine

To Solve: The equation $c^2-4c-2=0$ and to write the irrational roots in the simplest form.

Answer to Problem 10MRE

The required answer is $\left\{2+\sqrt{6},2-\sqrt{6}\right\}$ .

Explanation of Solution

Given information:

The equation $c^2-4c-2=0$

Calculation:

  $\begin{array}{l}{c}^2-4c-2=0\\ c^2-4c=2\end{array}$

(Add 2 to each side and rewrite the equation)

  $c^2-4c+{\left(-2\right)}^2=2+{\left(-2\right)}^2$

(Add Square of half the coefficient of c)

  $\begin{array}{l}{c}^2-4c+4=2+4\\ {\left(c-2\right)}^2=6\end{array}$

(Simplify)

  $c-2=\pm \sqrt{6}$

(Perform square roots on both sides)

  $c=2\pm \sqrt{6}$

So,

  $c=2+\sqrt{6}$

Or

  $c=2-\sqrt{6}$

Therefore, the solution set is $\left\{2+\sqrt{6},2-\sqrt{6}\right\}$ .