What are the approximate solutions of #5x^2 − 7x = 1# rounded to the nearest hundredth?
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:
This is almost certainly good enough for the accuracy requested.
then use the Quadratic Formula for roots:
In this case
Using a calculator: