Chapter 4.2, Problem 1CFU

To determine

To write: A short paragraph about solving $t^2-6t-4=0$ by completing the square.

Answer to Problem 1CFU

  $t_1=3+\sqrt{13};t_2=3-\sqrt{13}$

Explanation of Solution

Given information: $t^2-6t-4=0$

Calculation:

We’ll write the quadratic considering the special product that gives the perfect square.

  $t^2-6t-4=t^2-2\times 3\times t+9-9-4=0$

We’ve combined the first three terms because they create a perfect square. The numbers alone are also combined.

  ${\left(t-3\right)}^2-13=0$

We’ve added 13 both sides to isolate the perfect square to the left side.

  ${\left(t-3\right)}^2-13+13=0+13$

We’ve taken the square root both sides.

  $\left(t-3\right)=\pm \sqrt{13}$

We’ve isolated t to the left side and we’ve get two roots: $t_1\text{ and }{t}_2$

  $t_1=3+\sqrt{13};t_2=3-\sqrt{13}$