x^2-14+5(x-121(21-x))=3(x-24)+41-x(24-1(41-313))

Solution for x^2-14+5(x-121(21-x))=3(x-24)+41-x(24-1(41-313)) equation:

Simplifying
x2 + -14 + 5(x + -121(21 + -1x)) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))
x2 + -14 + 5(x + (21 * -121 + -1x * -121)) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))
x2 + -14 + 5(x + (-2541 + 121x)) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))

Reorder the terms:
x2 + -14 + 5(-2541 + x + 121x) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))

Combine like terms: x + 121x = 122x
x2 + -14 + 5(-2541 + 122x) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))
x2 + -14 + (-2541 * 5 + 122x * 5) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))
x2 + -14 + (-12705 + 610x) = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))

Reorder the terms:
-14 + -12705 + 610x + x2 = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))

Combine like terms: -14 + -12705 = -12719
-12719 + 610x + x2 = 3(x + -24) + 41 + -1x(24 + -1(41 + -313))

Reorder the terms:
-12719 + 610x + x2 = 3(-24 + x) + 41 + -1x(24 + -1(41 + -313))
-12719 + 610x + x2 = (-24 * 3 + x * 3) + 41 + -1x(24 + -1(41 + -313))
-12719 + 610x + x2 = (-72 + 3x) + 41 + -1x(24 + -1(41 + -313))

Combine like terms: 41 + -313 = -272
-12719 + 610x + x2 = -72 + 3x + 41 + -1x(24 + -1(-272))

Multiply -1 * -272
-12719 + 610x + x2 = -72 + 3x + 41 + -1x(24 + 272)

Combine like terms: 24 + 272 = 296
-12719 + 610x + x2 = -72 + 3x + 41 + -1x(296)

Reorder the terms for easier multiplication:
-12719 + 610x + x2 = -72 + 3x + 41 + -1 * 296x

Multiply -1 * 296
-12719 + 610x + x2 = -72 + 3x + 41 + -296x

Reorder the terms:
-12719 + 610x + x2 = -72 + 41 + 3x + -296x

Combine like terms: -72 + 41 = -31
-12719 + 610x + x2 = -31 + 3x + -296x

Combine like terms: 3x + -296x = -293x
-12719 + 610x + x2 = -31 + -293x

Solving
-12719 + 610x + x2 = -31 + -293x

Solving for variable 'x'.

Reorder the terms:
-12719 + 31 + 610x + 293x + x2 = -31 + -293x + 31 + 293x

Combine like terms: -12719 + 31 = -12688
-12688 + 610x + 293x + x2 = -31 + -293x + 31 + 293x

Combine like terms: 610x + 293x = 903x
-12688 + 903x + x2 = -31 + -293x + 31 + 293x

Reorder the terms:
-12688 + 903x + x2 = -31 + 31 + -293x + 293x

Combine like terms: -31 + 31 = 0
-12688 + 903x + x2 = 0 + -293x + 293x
-12688 + 903x + x2 = -293x + 293x

Combine like terms: -293x + 293x = 0
-12688 + 903x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12688' to each side of the equation.
-12688 + 903x + 12688 + x2 = 0 + 12688

Reorder the terms:
-12688 + 12688 + 903x + x2 = 0 + 12688

Combine like terms: -12688 + 12688 = 0
0 + 903x + x2 = 0 + 12688
903x + x2 = 0 + 12688

Combine like terms: 0 + 12688 = 12688
903x + x2 = 12688

The x term is 903x.  Take half its coefficient (451.5).
Square it (203852.25) and add it to both sides.

Add '203852.25' to each side of the equation.
903x + 203852.25 + x2 = 12688 + 203852.25

Reorder the terms:
203852.25 + 903x + x2 = 12688 + 203852.25

Combine like terms: 12688 + 203852.25 = 216540.25
203852.25 + 903x + x2 = 216540.25

Factor a perfect square on the left side:
(x + 451.5)(x + 451.5) = 216540.25

Calculate the square root of the right side: 465.338855029

Break this problem into two subproblems by setting 
(x + 451.5) equal to 465.338855029 and -465.338855029.

Subproblem 1
x + 451.5 = 465.338855029

Simplifying
x + 451.5 = 465.338855029

Reorder the terms:
451.5 + x = 465.338855029

Solving
451.5 + x = 465.338855029

Solving for variable 'x'.

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

Add '-451.5' to each side of the equation.
451.5 + -451.5 + x = 465.338855029 + -451.5

Combine like terms: 451.5 + -451.5 = 0.0
0.0 + x = 465.338855029 + -451.5
x = 465.338855029 + -451.5

Combine like terms: 465.338855029 + -451.5 = 13.838855029
x = 13.838855029

Simplifying
x = 13.838855029

Subproblem 2
x + 451.5 = -465.338855029

Simplifying
x + 451.5 = -465.338855029

Reorder the terms:
451.5 + x = -465.338855029

Solving
451.5 + x = -465.338855029

Solving for variable 'x'.

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

Add '-451.5' to each side of the equation.
451.5 + -451.5 + x = -465.338855029 + -451.5

Combine like terms: 451.5 + -451.5 = 0.0
0.0 + x = -465.338855029 + -451.5
x = -465.338855029 + -451.5

Combine like terms: -465.338855029 + -451.5 = -916.838855029
x = -916.838855029

Simplifying
x = -916.838855029

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.838855029, -916.838855029}