Question

x-(x-1)²-5(x-1)-6=0 solve for x

Answer 1

We know that (a-b)^2 = a^2 + b^2 - 2ab.

Given Equation is x - (x - 1)^2 - 5(x - 1) - 6 = 0

                             = x - (x^2 + 1 - 2x) - 5x + 5 - 6 = 0

                             = x - x^2 - 1 + 2x - 5x - 1 = 0

                            = -x^2 - 2x - 2 = 0


By using Quadratic Equation, we get

x = $\frac{-b+ \sqrt{b^2 - 4ac} }{2a}$

   = $\frac{-(-2) + \sqrt{(-2)^2 - 4(-1)(-2)} }{2(-1)}$

   = $\frac{2 + \sqrt{4}i }{-2}$

   = -1 - i.


x = $\frac{-b- \sqrt{b^2-4ac} }{2a}$

   = $\frac{2 - \sqrt{(-2)^2 - 4(-1)(-2)} }{-2}$

   = $\frac{2 - 2i}{2}$

   = $\frac{-2(1 - i)}{2}$

   = -(1 - i)

   = -1 + i.


Hope this helps!