Answer:
Given the quadratic equation: [tex]11x^2- 4x = 1[/tex]
we can write this equation as;
[tex]11x^2-4x-1 = 0[/tex] ......[1]
A quadratic equation is in the form of [tex]ax^2+bx+c =0[/tex] where a, b , c are coefficient and
the solution for this equation is given by;
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] 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;
[tex]x = \frac{-(-4)\pm\sqrt{(-4)^2-4(11)(-1)}}{2(11)}[/tex]
[tex]x = \frac{ 4\pm\sqrt{16+44}}{22}[/tex]
[tex]x = \frac{ 4\pm\sqrt{60}}{22}[/tex]
or
[tex]x = \frac{ 4\pm 2\sqrt{15}}{22}[/tex]
[tex]x = \frac{ 2\pm \sqrt{15}}{11}[/tex]
Simplify:
[tex]x= \frac{2 + \sqrt{15} }{11}[/tex] and [tex]x= \frac{2 - \sqrt{15} }{11}[/tex]
Therefore, the values of x are;
[tex]x= \frac{2 + \sqrt{15} }{11}[/tex] , [tex]\frac{2 - \sqrt{15} }{11}[/tex]
