Chapter 9.5, Problem 6LC

To determine

To evaluate: how solving a quadratic equation using square roots likes completing the square and how it is different.

Explanation of Solution

Assume quadratic equation as,

  $k^2-6k+9=0$

Applying completing the square method to solve the above equation,

  $\begin{array}{c}{k}^2-6k+9=0\\ k^2-3k-3k+9=0\\ {\left(k-3\right)}^2=0\\ \left(k-3\right)=0\\ k=3\end{array}$

The solution of the above equation is $k=3$ .

Applying the square roots to solve the above equation,

Assume quadratic equation as,

  $k^2-4=0$

Applying the square roots to solve the above equation,

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

Both the methods are similar as they are used to find the solution.

Both the methods are different as they use different process to find the solution.