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;
\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\) 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;
\(x = \frac{-(-4)\pm\sqrt{(-4)^2-4(11)(-1)}}{2(11)}\)
\(x = \frac{ 4\pm\sqrt{16+44}}{22}\)
\(x = \frac{ 4\pm\sqrt{60}}{22}\)
or
\(x = \frac{ 4\pm 2\sqrt{15}}{22}\)
\(x = \frac{ 2\pm \sqrt{15}}{11}\)
Simplify:
\(x= \frac{2 + \sqrt{15} }{11}\) and \(x= \frac{2 - \sqrt{15} }{11}\)
Therefore, the values of x are;
\(x= \frac{2 + \sqrt{15} }{11}\) , \(\frac{2 - \sqrt{15} }{11}\)
