x+2x(5)+2x(2x)(10)+2x(2x)-3(25)+2x(100)+2x(500)=9382

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Solution for x+2x(5)+2x(2x)(10)+2x(2x)-3(25)+2x(100)+2x(500)=9382 equation:


Simplifying
x + 2x(5) + 2x(2x)(10) + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Reorder the terms for easier multiplication:
x + 2 * 5x + 2x(2x)(10) + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Multiply 2 * 5
x + 10x + 2x(2x)(10) + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Remove parenthesis around (2x)
x + 10x + 2x * 2x(10) + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Reorder the terms for easier multiplication:
x + 10x + 2 * 2 * 10x * x + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Multiply 2 * 2
x + 10x + 4 * 10x * x + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Multiply 4 * 10
x + 10x + 40x * x + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Multiply x * x
x + 10x + 40x2 + 2x(2x) + -3(25) + 2x(100) + 2x(500) = 9382

Remove parenthesis around (2x)
x + 10x + 40x2 + 2x * 2x + -3(25) + 2x(100) + 2x(500) = 9382

Reorder the terms for easier multiplication:
x + 10x + 40x2 + 2 * 2x * x + -3(25) + 2x(100) + 2x(500) = 9382

Multiply 2 * 2
x + 10x + 40x2 + 4x * x + -3(25) + 2x(100) + 2x(500) = 9382

Multiply x * x
x + 10x + 40x2 + 4x2 + -3(25) + 2x(100) + 2x(500) = 9382

Multiply -3 * 25
x + 10x + 40x2 + 4x2 + -75 + 2x(100) + 2x(500) = 9382

Reorder the terms for easier multiplication:
x + 10x + 40x2 + 4x2 + -75 + 2 * 100x + 2x(500) = 9382

Multiply 2 * 100
x + 10x + 40x2 + 4x2 + -75 + 200x + 2x(500) = 9382

Reorder the terms for easier multiplication:
x + 10x + 40x2 + 4x2 + -75 + 200x + 2 * 500x = 9382

Multiply 2 * 500
x + 10x + 40x2 + 4x2 + -75 + 200x + 1000x = 9382

Reorder the terms:
-75 + x + 10x + 200x + 1000x + 40x2 + 4x2 = 9382

Combine like terms: x + 10x = 11x
-75 + 11x + 200x + 1000x + 40x2 + 4x2 = 9382

Combine like terms: 11x + 200x = 211x
-75 + 211x + 1000x + 40x2 + 4x2 = 9382

Combine like terms: 211x + 1000x = 1211x
-75 + 1211x + 40x2 + 4x2 = 9382

Combine like terms: 40x2 + 4x2 = 44x2
-75 + 1211x + 44x2 = 9382

Solving
-75 + 1211x + 44x2 = 9382

Solving for variable 'x'.

Reorder the terms:
-75 + -9382 + 1211x + 44x2 = 9382 + -9382

Combine like terms: -75 + -9382 = -9457
-9457 + 1211x + 44x2 = 9382 + -9382

Combine like terms: 9382 + -9382 = 0
-9457 + 1211x + 44x2 = 0

Begin completing the square.  Divide all terms by
44 the coefficient of the squared term: 

Divide each side by '44'.
-214.9318182 + 27.52272727x + x2 = 0

Move the constant term to the right:

Add '214.9318182' to each side of the equation.
-214.9318182 + 27.52272727x + 214.9318182 + x2 = 0 + 214.9318182

Reorder the terms:
-214.9318182 + 214.9318182 + 27.52272727x + x2 = 0 + 214.9318182

Combine like terms: -214.9318182 + 214.9318182 = 0.0000000
0.0000000 + 27.52272727x + x2 = 0 + 214.9318182
27.52272727x + x2 = 0 + 214.9318182

Combine like terms: 0 + 214.9318182 = 214.9318182
27.52272727x + x2 = 214.9318182

The x term is 27.52272727x.  Take half its coefficient (13.76136364).
Square it (189.3751292) and add it to both sides.

Add '189.3751292' to each side of the equation.
27.52272727x + 189.3751292 + x2 = 214.9318182 + 189.3751292

Reorder the terms:
189.3751292 + 27.52272727x + x2 = 214.9318182 + 189.3751292

Combine like terms: 214.9318182 + 189.3751292 = 404.3069474
189.3751292 + 27.52272727x + x2 = 404.3069474

Factor a perfect square on the left side:
(x + 13.76136364)(x + 13.76136364) = 404.3069474

Calculate the square root of the right side: 20.107385394

Break this problem into two subproblems by setting 
(x + 13.76136364) equal to 20.107385394 and -20.107385394.

Subproblem 1

x + 13.76136364 = 20.107385394 Simplifying x + 13.76136364 = 20.107385394 Reorder the terms: 13.76136364 + x = 20.107385394 Solving 13.76136364 + x = 20.107385394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.76136364' to each side of the equation. 13.76136364 + -13.76136364 + x = 20.107385394 + -13.76136364 Combine like terms: 13.76136364 + -13.76136364 = 0.00000000 0.00000000 + x = 20.107385394 + -13.76136364 x = 20.107385394 + -13.76136364 Combine like terms: 20.107385394 + -13.76136364 = 6.346021754 x = 6.346021754 Simplifying x = 6.346021754

Subproblem 2

x + 13.76136364 = -20.107385394 Simplifying x + 13.76136364 = -20.107385394 Reorder the terms: 13.76136364 + x = -20.107385394 Solving 13.76136364 + x = -20.107385394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.76136364' to each side of the equation. 13.76136364 + -13.76136364 + x = -20.107385394 + -13.76136364 Combine like terms: 13.76136364 + -13.76136364 = 0.00000000 0.00000000 + x = -20.107385394 + -13.76136364 x = -20.107385394 + -13.76136364 Combine like terms: -20.107385394 + -13.76136364 = -33.868749034 x = -33.868749034 Simplifying x = -33.868749034

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.346021754, -33.868749034}

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