# What are the approximate solutions of #5x^2 − 7x = 1# rounded to the nearest hundredth?

##### 2 Answers

Subtracting

This is of the form

The general formula for roots of such a quadratic gives us:

What is a good approximation for

We could punch it into a calculator, but let's do it by hand instead using Newton-Raphson:

Then iterate using the formula:

Let

This is almost certainly good enough for the accuracy requested.

So

That is

Rewrite

giving

then use the Quadratic Formula for roots:

In this case

Using a calculator:

So

or