Chapter 4, Problem 32AR

To determine

To solve the given equation, $2x^2-7x-4=0$ by factoring or quadratic formula where x represents the length of a segment.

Answer to Problem 32AR

  $x=4$

Explanation of Solution

Given:

The equation is, $2x^2-7x-4=0$

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 $2x^2-7x-4=0$ , which is in the form of $a{x}^2+bx+c=0$ . Where, $a=2,b=-7\text{ and c =-4}$

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

  $\begin{array}{l}x=\frac{-\left(-7\right)\pm \sqrt{{\left(-7\right)}^2-4\left(2\right)\left(-4\right)}}{2\left(2\right)}\\ x=\frac{7\pm \sqrt{49+32}}{4}\\ x=\frac{7\pm \sqrt{81}}{4}\\ x=\frac{7\pm 9}{4}\\ x=\frac{7+9}{4},\frac{7-9}{4}\\ x=\frac{16}{4},\frac{-2}{4}\\ x=4,\frac{-1}{2}\end{array}$

Here, the x is having two values. $x=4$ and $x=\frac{-1}{2}$ . In the question given that x is a length of a segment so x should not be negative.

Therefore, the value of x is 4.