Chapter 4, Problem 14AR

To determine

To solve the given equation, $t^2+5t=24$ by factoring or quadratic formula.

Answer to Problem 14AR

  $x=3,-8$

Explanation of Solution

Given:

The equation is, $t^2+5t=24$

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,

  $\begin{array}{l}{t}^2+5t=24\\ t^2+5t-24=0\end{array}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=5\text{ and c = -24}$ .

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

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(5\right)\pm \sqrt{{\left(5\right)}^2-4\left(1\right)\left(-24\right)}}{2\left(1\right)}\\ x=\frac{-5\pm \sqrt{25+96}}{2}\\ x=\frac{-5\pm \sqrt{121}}{2}\\ x=\frac{-5\pm 11}{2}\\ x=\frac{-5+11}{2},\frac{-5-11}{2}\\ x=\frac{6}{2},\frac{-16}{2}\\ x=3,-8\end{array}$

Therefore, the roots for the given equation, $t^2+5t=24$ are $x=3,-8$ .