Chapter 12.3, Problem 10MRE

To determine

To Solve: The equation $y^2-10y+16=0$ by completing the square.

Answer to Problem 10MRE

The required solution set is $\left\{8,2\right\}$

Explanation of Solution

Given information:

  $y^2-10y+16=0$

Calculation:

  $\begin{array}{l}{y}^2-10y+16=0\\ y^2-10y=-16\end{array}$

(Subtract 16 from each side and rewrite the equation)

  $y^2-10y+{\left(-5\right)}^2=-16+{\left(-5\right)}^2$

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

  $\begin{array}{l}{y}^2-10y+25=-16+25\\ {\left(y-5\right)}^2=9\end{array}$

(Simplify)

  $\begin{array}{l}y-5=\sqrt{9}\\ y-5=\pm 3\end{array}$

(Perform square root on both sides)

  $y=5\pm 3$

So,

  $\begin{array}{l}y=5+3\\ y=8\end{array}$

Or

  $\begin{array}{l}y=5-3\\ y=2\end{array}$

Therefore, the required solution set is $\left\{8,2\right\}$ .