Question

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

Answer 1

`(2)/(11) +/- ( √(15) )/(11)`

Answer 2

Given the quadratic equation:
`11x^2- 4x = 1`

we can write this equation as;

`11x^2-4x-1 = 0` ......[1]

A quadratic equation is in the form of
`ax^2+bx+c =0` where a, b , c are coefficient and

the solution for this equation is given by;

`x = (-b\pm√(b^2-4ac))/(2a)` where a≠0

On comparing the above formula with an equation [1] we have;

a = 11 , b = -4 and c =-1

Substitute these given values to solve for x;

`x = (-(-4)\pm√((-4)^2-4(11)(-1)))/(2(11))`

`x = ( 4\pm√(16+44))/(22)`

`x = ( 4\pm√(60))/(22)`

or

`x = ( 4\pm 2√(15))/(22)`

`x = ( 2\pm √(15))/(11)`

Simplify:

`x= (2 + √(15) )/(11)` and
`x= (2 - √(15) )/(11)`

Therefore, the values of x are;

`x= (2 + √(15) )/(11)` ,
`(2 - √(15) )/(11)`