x+(x-1)x+(x-1)=77

Solution for x+(x-1)x+(x-1)=77 equation:

Simplifying
x + (x + -1) * x + (x + -1) = 77

Reorder the terms:
x + (-1 + x) * x + (x + -1) = 77

Reorder the terms for easier multiplication:
x + x(-1 + x) + (x + -1) = 77
x + (-1 * x + x * x) + (x + -1) = 77
x + (-1x + x2) + (x + -1) = 77

Reorder the terms:
x + -1x + x2 + (-1 + x) = 77

Remove parenthesis around (-1 + x)
x + -1x + x2 + -1 + x = 77

Reorder the terms:
-1 + x + -1x + x + x2 = 77

Combine like terms: x + -1x = 0
-1 + 0 + x + x2 = 77
-1 + x + x2 = 77

Solving
-1 + x + x2 = 77

Solving for variable 'x'.

Reorder the terms:
-1 + -77 + x + x2 = 77 + -77

Combine like terms: -1 + -77 = -78
-78 + x + x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-78 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + x + x2 = 0 + 78
x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
x + x2 = 78

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 78 + 0.25

Reorder the terms:
0.25 + x + x2 = 78 + 0.25

Combine like terms: 78 + 0.25 = 78.25
0.25 + x + x2 = 78.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.845903006 and -8.845903006.

Subproblem 1
x + 0.5 = 8.845903006

Simplifying
x + 0.5 = 8.845903006

Reorder the terms:
0.5 + x = 8.845903006

Solving
0.5 + x = 8.845903006

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 8.845903006 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 8.845903006 + -0.5
x = 8.845903006 + -0.5

Combine like terms: 8.845903006 + -0.5 = 8.345903006
x = 8.345903006

Simplifying
x = 8.345903006

Subproblem 2
x + 0.5 = -8.845903006

Simplifying
x + 0.5 = -8.845903006

Reorder the terms:
0.5 + x = -8.845903006

Solving
0.5 + x = -8.845903006

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -8.845903006 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -8.845903006 + -0.5
x = -8.845903006 + -0.5

Combine like terms: -8.845903006 + -0.5 = -9.345903006
x = -9.345903006

Simplifying
x = -9.345903006

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.345903006, -9.345903006}