Chapter 4, Problem 17AR

To determine

To solve the given equation, $t^2-t=20$ by factoring or quadratic formula.

Answer to Problem 17AR

  $x=5,x=-4$

Explanation of Solution

Given:

The equation is, $t^2-t=20$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, write the equation as,

  $\begin{array}{l}{t}^2-t=20\\ t^2-t-20=0\end{array}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=-1\text{ and c = -20}$ .

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-1\right)\pm \sqrt{{\left(1\right)}^2-4\left(1\right)\left(-20\right)}}{2\left(1\right)}\\ x=\frac{1\pm \sqrt{1+80}}{2}\\ x=\frac{1\pm 9}{2}\\ x=\frac{1+9}{2},x=\frac{1-9}{2}\\ x=5,x=-4\end{array}$

Therefore, the roots for the given equation, $t^2-t=20$ are $x=5,x=-4$ .