Chapter 4, Problem 30AR

To determine

To solve the given equation, $x^2-17x+72=0$ by factoring or quadratic formula where x represents the length of a segment.

Answer to Problem 30AR

  $x=9,8$

Explanation of Solution

Given:

The equation is, $x^2-17x+72=0$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, the equation $x^2-17x+72=0$ , which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=-17\text{ and c =72}$

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

  $\begin{array}{l}x=\frac{-\left(-17\right)\pm \sqrt{{\left(-17\right)}^2-4\left(1\right)\left(72\right)}}{2\left(1\right)}\\ x=\frac{17\pm \sqrt{289-288}}{2}\\ x=\frac{17\pm \sqrt{1}}{2}\\ x=\frac{17+\sqrt{1}}{2},\frac{17-\sqrt{1}}{2}\\ x=\frac{17+1}{2},\frac{17-1}{2}\\ x=\frac{18}{2},\frac{16}{2}\\ x=9,8\end{array}$

Here, the x is having two values. 9 and 8. In the question given that x is a length of a segment and both values are legible.

Therefore, the value of x is 8and 9.