2(x-10)-10(x+9)=x(x-1)+50

Solution for 2(x-10)-10(x+9)=x(x-1)+50 equation:

Simplifying
2(x + -10) + -10(x + 9) = x(x + -1) + 50

Reorder the terms:
2(-10 + x) + -10(x + 9) = x(x + -1) + 50
(-10 * 2 + x * 2) + -10(x + 9) = x(x + -1) + 50
(-20 + 2x) + -10(x + 9) = x(x + -1) + 50

Reorder the terms:
-20 + 2x + -10(9 + x) = x(x + -1) + 50
-20 + 2x + (9 * -10 + x * -10) = x(x + -1) + 50
-20 + 2x + (-90 + -10x) = x(x + -1) + 50

Reorder the terms:
-20 + -90 + 2x + -10x = x(x + -1) + 50

Combine like terms: -20 + -90 = -110
-110 + 2x + -10x = x(x + -1) + 50

Combine like terms: 2x + -10x = -8x
-110 + -8x = x(x + -1) + 50

Reorder the terms:
-110 + -8x = x(-1 + x) + 50
-110 + -8x = (-1 * x + x * x) + 50
-110 + -8x = (-1x + x2) + 50

Reorder the terms:
-110 + -8x = 50 + -1x + x2

Solving
-110 + -8x = 50 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-110 + -50 + -8x + x + -1x2 = 50 + -1x + x2 + -50 + x + -1x2

Combine like terms: -110 + -50 = -160
-160 + -8x + x + -1x2 = 50 + -1x + x2 + -50 + x + -1x2

Combine like terms: -8x + x = -7x
-160 + -7x + -1x2 = 50 + -1x + x2 + -50 + x + -1x2

Reorder the terms:
-160 + -7x + -1x2 = 50 + -50 + -1x + x + x2 + -1x2

Combine like terms: 50 + -50 = 0
-160 + -7x + -1x2 = 0 + -1x + x + x2 + -1x2
-160 + -7x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-160 + -7x + -1x2 = 0 + x2 + -1x2
-160 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-160 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(160 + 7x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(160 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
160 + 7x + x2 = 0

Solving
160 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-160' to each side of the equation.
160 + 7x + -160 + x2 = 0 + -160

Reorder the terms:
160 + -160 + 7x + x2 = 0 + -160

Combine like terms: 160 + -160 = 0
0 + 7x + x2 = 0 + -160
7x + x2 = 0 + -160

Combine like terms: 0 + -160 = -160
7x + x2 = -160

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -160 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -160 + 12.25

Combine like terms: -160 + 12.25 = -147.75
12.25 + 7x + x2 = -147.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = -147.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.