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:

`(-b_-^+ √(b^2-4ac) )/(2a)`

Now plug in the values of a,b,c

`(-(-4)_-^+ √((-4)^2-4(11)(-1)) )/(2(11))`

Simplify it:

`(4_-^+ √(60) )/(22)`

You can further simplify the given equation to get a final answer of:

`x= (2)/(11)+ (1)/(11) √(15)`

or

`x= (2)/(11)+ (-1)/(11) √(15)`