Quadratic equation with n number of repeated terms as coefficient

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Solution:

Let 11......11 = a,

Put this value in our equation:

8ax² + 4ax = 2a

: 8x² + 4x = 2

: 4x² + 2x = 1

: 4x² + 2x - 1 = 0

By quadratic formula:

\[x = \frac{-2 \pm \sqrt{2^2-4(4)(-1)}}{2(4)}\]

\[\Rightarrow x = \frac{-1 \pm \sqrt5}4\]