ex1.5_14

Example

$x$ $\quad 4x^2+x-4=0$ . Round your answer(s) to the nearest hundredth.

Solution

We should start by trying to factor, but we will quickly see that the expression on the left cannot be factored over the integers. Let's use the quadratic formula.

In this problem, we have

a=4, \, b=1, \, c=-4.

It follows that

x = \frac{-(1) \pm \sqrt{(1)^2-4(4)(-4)}}{2(4)}

x = \frac{-1 \pm \sqrt{65}}{8}.

Since we are asked to give decimal answers, it is not worth trying to simplify our answers. Let's just go straight to the calculator. There are two solutions,

x=\frac{-1+\sqrt{65}}{8} \approx 0.88

x=\frac{-1-\sqrt{65}}{8} \approx -1.13.