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

Question

asked Dec 7, 2017 145k views

2 Answers

Aram Hovhannisyan · Answer 1 · 2017-12-13T20:35:01+0000

Answer:

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)