Chapter 4, Problem 33AR

To determine

To solve the given equation, $6x^2=5x+6$ by factoring or quadratic formula where x represents the length of a segment.

Answer to Problem 33AR

  $x=\frac{3}{2}$

Explanation of Solution

Given:

The equation is, $6x^2=5x+6$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

We can write the given equation as

  $\begin{array}{l}6x^2=5x+6\\ 6x^2-5x-6=0\end{array}$

Now, the equation $6x^2-5x-6=0$ , which is in the form of $a{x}^2+bx+c=0$ . Where, $a=6,b=-5\text{ and c =-6}$

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

  $\begin{array}{l}x=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\left(6\right)\left(-6\right)}}{2\left(6\right)}\\ x=\frac{5\pm \sqrt{25+144}}{12}\\ x=\frac{5\pm \sqrt{169}}{12}\\ x=\frac{5\pm 13}{12}\\ x=\frac{5+13}{12},\frac{5-13}{12}\\ x=\frac{18}{12},\frac{-8}{12}\\ x=\frac{3}{2},\frac{-2}{3}\end{array}$

Here, the x is having two values. $x=\frac{3}{2}$ and $x=\frac{-2}{3}$ . In the question given that x is a length of a segment so x should not be negative.

Therefore, the value of x is, $x=\frac{3}{2}$ .