283(x-24(234-x))(x-24)=2x(45021-41234)(45021+41234)-x(4-4x)

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Solution for 283(x-24(234-x))(x-24)=2x(45021-41234)(45021+41234)-x(4-4x) equation:


Simplifying
283(x + -24(234 + -1x))(x + -24) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
283(x + (234 * -24 + -1x * -24))(x + -24) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
283(x + (-5616 + 24x))(x + -24) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)

Reorder the terms:
283(-5616 + x + 24x)(x + -24) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)

Combine like terms: x + 24x = 25x
283(-5616 + 25x)(x + -24) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)

Reorder the terms:
283(-5616 + 25x)(-24 + x) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)

Multiply (-5616 + 25x) * (-24 + x)
283(-5616(-24 + x) + 25x * (-24 + x)) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
283((-24 * -5616 + x * -5616) + 25x * (-24 + x)) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
283((134784 + -5616x) + 25x * (-24 + x)) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
283(134784 + -5616x + (-24 * 25x + x * 25x)) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
283(134784 + -5616x + (-600x + 25x2)) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)

Combine like terms: -5616x + -600x = -6216x
283(134784 + -6216x + 25x2) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
(134784 * 283 + -6216x * 283 + 25x2 * 283) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)
(38143872 + -1759128x + 7075x2) = 2x(45021 + -41234)(45021 + 41234) + -1x(4 + -4x)

Combine like terms: 45021 + -41234 = 3787
38143872 + -1759128x + 7075x2 = 2x(3787)(45021 + 41234) + -1x(4 + -4x)

Combine like terms: 45021 + 41234 = 86255
38143872 + -1759128x + 7075x2 = 2x * 3787(86255) + -1x(4 + -4x)

Reorder the terms for easier multiplication:
38143872 + -1759128x + 7075x2 = 2 * 3787 * 86255x + -1x(4 + -4x)

Multiply 2 * 3787
38143872 + -1759128x + 7075x2 = 7574 * 86255x + -1x(4 + -4x)

Multiply 7574 * 86255
38143872 + -1759128x + 7075x2 = 653295370x + -1x(4 + -4x)
38143872 + -1759128x + 7075x2 = 653295370x + (4 * -1x + -4x * -1x)
38143872 + -1759128x + 7075x2 = 653295370x + (-4x + 4x2)

Combine like terms: 653295370x + -4x = 653295366x
38143872 + -1759128x + 7075x2 = 653295366x + 4x2

Solving
38143872 + -1759128x + 7075x2 = 653295366x + 4x2

Solving for variable 'x'.

Reorder the terms:
38143872 + -1759128x + -653295366x + 7075x2 + -4x2 = 653295366x + 4x2 + -653295366x + -4x2

Combine like terms: -1759128x + -653295366x = -655054494x
38143872 + -655054494x + 7075x2 + -4x2 = 653295366x + 4x2 + -653295366x + -4x2

Combine like terms: 7075x2 + -4x2 = 7071x2
38143872 + -655054494x + 7071x2 = 653295366x + 4x2 + -653295366x + -4x2

Reorder the terms:
38143872 + -655054494x + 7071x2 = 653295366x + -653295366x + 4x2 + -4x2

Combine like terms: 653295366x + -653295366x = 0
38143872 + -655054494x + 7071x2 = 0 + 4x2 + -4x2
38143872 + -655054494x + 7071x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
38143872 + -655054494x + 7071x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12714624 + -218351498x + 2357x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(12714624 + -218351498x + 2357x2)' equal to zero and attempt to solve: Simplifying 12714624 + -218351498x + 2357x2 = 0 Solving 12714624 + -218351498x + 2357x2 = 0 Begin completing the square. Divide all terms by 2357 the coefficient of the squared term: Divide each side by '2357'. 5394.409843 + -92639.58337x + x2 = 0 Move the constant term to the right: Add '-5394.409843' to each side of the equation. 5394.409843 + -92639.58337x + -5394.409843 + x2 = 0 + -5394.409843 Reorder the terms: 5394.409843 + -5394.409843 + -92639.58337x + x2 = 0 + -5394.409843 Combine like terms: 5394.409843 + -5394.409843 = 0.000000 0.000000 + -92639.58337x + x2 = 0 + -5394.409843 -92639.58337x + x2 = 0 + -5394.409843 Combine like terms: 0 + -5394.409843 = -5394.409843 -92639.58337x + x2 = -5394.409843 The x term is -92639.58337x. Take half its coefficient (-46319.79169). Square it (2145523102) and add it to both sides. Add '2145523102' to each side of the equation. -92639.58337x + 2145523102 + x2 = -5394.409843 + 2145523102 Reorder the terms: 2145523102 + -92639.58337x + x2 = -5394.409843 + 2145523102 Combine like terms: -5394.409843 + 2145523102 = 2145517707.590157 2145523102 + -92639.58337x + x2 = 2145517707.590157 Factor a perfect square on the left side: (x + -46319.79169)(x + -46319.79169) = 2145517707.590157 Calculate the square root of the right side: 46319.733457676 Break this problem into two subproblems by setting (x + -46319.79169) equal to 46319.733457676 and -46319.733457676.

Subproblem 1

x + -46319.79169 = 46319.733457676 Simplifying x + -46319.79169 = 46319.733457676 Reorder the terms: -46319.79169 + x = 46319.733457676 Solving -46319.79169 + x = 46319.733457676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46319.79169' to each side of the equation. -46319.79169 + 46319.79169 + x = 46319.733457676 + 46319.79169 Combine like terms: -46319.79169 + 46319.79169 = 0.00000 0.00000 + x = 46319.733457676 + 46319.79169 x = 46319.733457676 + 46319.79169 Combine like terms: 46319.733457676 + 46319.79169 = 92639.525147676 x = 92639.525147676 Simplifying x = 92639.525147676

Subproblem 2

x + -46319.79169 = -46319.733457676 Simplifying x + -46319.79169 = -46319.733457676 Reorder the terms: -46319.79169 + x = -46319.733457676 Solving -46319.79169 + x = -46319.733457676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46319.79169' to each side of the equation. -46319.79169 + 46319.79169 + x = -46319.733457676 + 46319.79169 Combine like terms: -46319.79169 + 46319.79169 = 0.00000 0.00000 + x = -46319.733457676 + 46319.79169 x = -46319.733457676 + 46319.79169 Combine like terms: -46319.733457676 + 46319.79169 = 0.058232324 x = 0.058232324 Simplifying x = 0.058232324

Solution

The solution to the problem is based on the solutions from the subproblems. x = {92639.525147676, 0.058232324}

Solution

x = {92639.525147676, 0.058232324}

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