x+(2x-8)+(3x-6)+x(x+10)=360

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Solution for x+(2x-8)+(3x-6)+x(x+10)=360 equation:


Simplifying
x + (2x + -8) + (3x + -6) + x(x + 10) = 360

Reorder the terms:
x + (-8 + 2x) + (3x + -6) + x(x + 10) = 360

Remove parenthesis around (-8 + 2x)
x + -8 + 2x + (3x + -6) + x(x + 10) = 360

Reorder the terms:
x + -8 + 2x + (-6 + 3x) + x(x + 10) = 360

Remove parenthesis around (-6 + 3x)
x + -8 + 2x + -6 + 3x + x(x + 10) = 360

Reorder the terms:
x + -8 + 2x + -6 + 3x + x(10 + x) = 360
x + -8 + 2x + -6 + 3x + (10 * x + x * x) = 360
x + -8 + 2x + -6 + 3x + (10x + x2) = 360

Reorder the terms:
-8 + -6 + x + 2x + 3x + 10x + x2 = 360

Combine like terms: -8 + -6 = -14
-14 + x + 2x + 3x + 10x + x2 = 360

Combine like terms: x + 2x = 3x
-14 + 3x + 3x + 10x + x2 = 360

Combine like terms: 3x + 3x = 6x
-14 + 6x + 10x + x2 = 360

Combine like terms: 6x + 10x = 16x
-14 + 16x + x2 = 360

Solving
-14 + 16x + x2 = 360

Solving for variable 'x'.

Reorder the terms:
-14 + -360 + 16x + x2 = 360 + -360

Combine like terms: -14 + -360 = -374
-374 + 16x + x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-374 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '374' to each side of the equation.
-374 + 16x + 374 + x2 = 0 + 374

Reorder the terms:
-374 + 374 + 16x + x2 = 0 + 374

Combine like terms: -374 + 374 = 0
0 + 16x + x2 = 0 + 374
16x + x2 = 0 + 374

Combine like terms: 0 + 374 = 374
16x + x2 = 374

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 374 + 64

Reorder the terms:
64 + 16x + x2 = 374 + 64

Combine like terms: 374 + 64 = 438
64 + 16x + x2 = 438

Factor a perfect square on the left side:
(x + 8)(x + 8) = 438

Calculate the square root of the right side: 20.928449536

Break this problem into two subproblems by setting 
(x + 8) equal to 20.928449536 and -20.928449536.

Subproblem 1

x + 8 = 20.928449536 Simplifying x + 8 = 20.928449536 Reorder the terms: 8 + x = 20.928449536 Solving 8 + x = 20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 20.928449536 + -8 Combine like terms: 8 + -8 = 0 0 + x = 20.928449536 + -8 x = 20.928449536 + -8 Combine like terms: 20.928449536 + -8 = 12.928449536 x = 12.928449536 Simplifying x = 12.928449536

Subproblem 2

x + 8 = -20.928449536 Simplifying x + 8 = -20.928449536 Reorder the terms: 8 + x = -20.928449536 Solving 8 + x = -20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -20.928449536 + -8 Combine like terms: 8 + -8 = 0 0 + x = -20.928449536 + -8 x = -20.928449536 + -8 Combine like terms: -20.928449536 + -8 = -28.928449536 x = -28.928449536 Simplifying x = -28.928449536

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.928449536, -28.928449536}

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