Chapter 12.2, Problem 9WE

To determine

To Solve: The equation $5x^2-20x=10$ by completing the square.

Answer to Problem 9WE

The required solution set is $\left\{2+\sqrt{6},2-\sqrt{6}\right\}$

Explanation of Solution

Given information:

  $5x^2-20x=10$

Calculation:

  $\begin{array}{l}5x^2-20x=10\\ x^2-4x=2\end{array}$

(Divide both sides by 5 so that the coefficient of $x^2$ will be 1)

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

(Add square of half the coefficient of x to both sides)

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

(Simplify)

  $x-2=\pm \sqrt{6}$

(Perform square root on both sides)

  $x=2\pm \sqrt{6}$

(Add 2 to each side)

  $x=2+\sqrt{6}$

Or

  $x=2-\sqrt{6}$

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

Now round off the solution to its nearest tenth

  $\begin{array}{l}x=2+\sqrt{6}\\ x=4.4\end{array}$

Or

  $\begin{array}{l}x=2-\sqrt{6}\\ x=-0.4\end{array}$