Question

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

Answer 1

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;

$x= \frac{2 + \sqrt{15} }{11}$ , $\frac{2 - \sqrt{15} }{11}$

Answer 2

$\frac{2}{11} +/- \frac{ \sqrt{15} }{11}$