Chapter 4, Problem 29AR

To determine

To solve the given equation, $x^2-400=0$ by factoring or quadratic formula where x represents the length of a segment.

Answer to Problem 29AR

  $x=20$

Explanation of Solution

Given:

The equation is, $x^2-400=0$

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 $x^2-400=0$ , which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=0\text{ and c =-400}$

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

  $\begin{array}{l}x=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\left(1\right)\left(-400\right)}}{2\left(1\right)}\\ x=\frac{\sqrt{1600}}{2}\\ x=\frac{\pm 40}{2}\\ x=\pm 20\end{array}$

Here, the x is having two values. 20 and -20. In the question given that x is a length of a segment that could not be negative.

Therefore, the value of x is 20.