Question

Using the quadratic formula to solve 11x^2 - 4x = 1, what are the values of x?

Answer 1

In order to get the a,b,c values for the quadratic formula we need to put the equation in standered form: 
$ax^2+bx+c=0$

We can do this by subtracting 1 from both sides: 
$11x^2-4x-1=1-1$

Now we have: 
$11x^2-4x-1=0$

a=11, b=-4, c=-1 

Now you use the quadratic formula: 
$\frac{-b_-^+ \sqrt{b^2-4ac} }{2a}$

Now plug in the values of a,b,c
$\frac{-(-4)_-^+ \sqrt{(-4)^2-4(11)(-1)} }{2(11)}$

Simplify it: 
$\frac{4_-^+ \sqrt{60} }{22}$

You can further simplify the given equation to get a final answer of: 
$x= \frac{2}{11}+ \frac{1}{11} \sqrt{15}$

or
 $x= \frac{2}{11}+ \frac{-1}{11} \sqrt{15}$