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Simplifying 2x2 + -3160x + 1279000 = 60000 Reorder the terms: 1279000 + -3160x + 2x2 = 60000 Solving 1279000 + -3160x + 2x2 = 60000 Solving for variable 'x'. Reorder the terms: 1279000 + -60000 + -3160x + 2x2 = 60000 + -60000 Combine like terms: 1279000 + -60000 = 1219000 1219000 + -3160x + 2x2 = 60000 + -60000 Combine like terms: 60000 + -60000 = 0 1219000 + -3160x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(609500 + -1580x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(609500 + -1580x + x2)' equal to zero and attempt to solve: Simplifying 609500 + -1580x + x2 = 0 Solving 609500 + -1580x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-609500' to each side of the equation. 609500 + -1580x + -609500 + x2 = 0 + -609500 Reorder the terms: 609500 + -609500 + -1580x + x2 = 0 + -609500 Combine like terms: 609500 + -609500 = 0 0 + -1580x + x2 = 0 + -609500 -1580x + x2 = 0 + -609500 Combine like terms: 0 + -609500 = -609500 -1580x + x2 = -609500 The x term is -1580x. Take half its coefficient (-790). Square it (624100) and add it to both sides. Add '624100' to each side of the equation. -1580x + 624100 + x2 = -609500 + 624100 Reorder the terms: 624100 + -1580x + x2 = -609500 + 624100 Combine like terms: -609500 + 624100 = 14600 624100 + -1580x + x2 = 14600 Factor a perfect square on the left side: (x + -790)(x + -790) = 14600 Calculate the square root of the right side: 120.830459736 Break this problem into two subproblems by setting (x + -790) equal to 120.830459736 and -120.830459736.Subproblem 1
x + -790 = 120.830459736 Simplifying x + -790 = 120.830459736 Reorder the terms: -790 + x = 120.830459736 Solving -790 + x = 120.830459736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = 120.830459736 + 790 Combine like terms: -790 + 790 = 0 0 + x = 120.830459736 + 790 x = 120.830459736 + 790 Combine like terms: 120.830459736 + 790 = 910.830459736 x = 910.830459736 Simplifying x = 910.830459736Subproblem 2
x + -790 = -120.830459736 Simplifying x + -790 = -120.830459736 Reorder the terms: -790 + x = -120.830459736 Solving -790 + x = -120.830459736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = -120.830459736 + 790 Combine like terms: -790 + 790 = 0 0 + x = -120.830459736 + 790 x = -120.830459736 + 790 Combine like terms: -120.830459736 + 790 = 669.169540264 x = 669.169540264 Simplifying x = 669.169540264Solution
The solution to the problem is based on the solutions from the subproblems. x = {910.830459736, 669.169540264}Solution
x = {910.830459736, 669.169540264}
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