Using the quadratic formula to solve 11x²-4x=1. Find the value of x?

Solution:

11x² - 4x = 1 [Given]

11x² - 4x - 1 = 0

The standard formula to evaluate the quadratic equation ax² + bx + c = 0 is

\( x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a} \)

By comparing the given equation to the standard form

a = 11

b = - 4

c = - 1

Substituting it in the equation

\( \\x = \frac{-(-4)\pm \sqrt{(-4)^{2}-4\times 11\times -1}}{2\times 11} \\ \\x=\frac{4\pm \sqrt{16+44}}{22} \\ \\x=\frac{4\pm \sqrt{60}}{22} \\ \\x=\frac{4\pm \sqrt{15\times 4}}{22} \)

\( \\x=\frac{4\pm 2\sqrt{15}}{22} \\ \\Taking \: out \: 2 \: as \: common \\ \\x=\frac{2\pm \sqrt{15}}{11} \\ \\x=\frac{2}{11}\pm \frac{\sqrt{15}}{11} \)

Therefore, the value of x is 2/11 ± √15/11.