(x-1)(x-1)+5=0

Solution for (x-1)(x-1)+5=0 equation:

Simplifying
(x + -1)(x + -1) + 5 = 0

Reorder the terms:
(-1 + x)(x + -1) + 5 = 0

Reorder the terms:
(-1 + x)(-1 + x) + 5 = 0

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + 5 = 0
((-1 * -1 + x * -1) + x(-1 + x)) + 5 = 0
((1 + -1x) + x(-1 + x)) + 5 = 0
(1 + -1x + (-1 * x + x * x)) + 5 = 0
(1 + -1x + (-1x + x2)) + 5 = 0

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + 5 = 0

Reorder the terms:
1 + 5 + -2x + x2 = 0

Combine like terms: 1 + 5 = 6
6 + -2x + x2 = 0

Solving
6 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -2x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -2x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -2x + x2 = 0 + -6
-2x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-2x + x2 = -6

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -6 + 1

Reorder the terms:
1 + -2x + x2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + -2x + x2 = -5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.