Question

In Exercises 28-33 xrepresents the length of a segment. When a value of xdoesn't make sense as a length, eliminate that value of x.

$x^2-400=0$

Short answer

The values of is$x=20$

Step-by-step solution

- Understand the concept used 

if$a{x}^2+bx+c=0$with$a\ne 0$then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values 

It is given that $x^2-400=0$Using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

, substitute 1 for a, 0 for b and -400 for c.

Put the values in the formula and get $x=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(1\right)\times \left(-400\right)}}{2\left(1\right)}$.

- Simplify for x 

Simplify the expression for x.

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

Therefore, either$x=\frac{40}{2}$or$x=\frac{-40}{2}$that is., either$x=20$or$x=20$ Here, the is having two values. 20 and -20. Since, is a length of a segment that could not be negative, therefore, the value of is 20.