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Simplifying 3x2 + 253x = 180000 + -19500 + -20000 Reorder the terms: 253x + 3x2 = 180000 + -19500 + -20000 Combine like terms: 180000 + -19500 = 160500 253x + 3x2 = 160500 + -20000 Combine like terms: 160500 + -20000 = 140500 253x + 3x2 = 140500 Solving 253x + 3x2 = 140500 Solving for variable 'x'. Reorder the terms: -140500 + 253x + 3x2 = 140500 + -140500 Combine like terms: 140500 + -140500 = 0 -140500 + 253x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -46833.33333 + 84.33333333x + x2 = 0 Move the constant term to the right: Add '46833.33333' to each side of the equation. -46833.33333 + 84.33333333x + 46833.33333 + x2 = 0 + 46833.33333 Reorder the terms: -46833.33333 + 46833.33333 + 84.33333333x + x2 = 0 + 46833.33333 Combine like terms: -46833.33333 + 46833.33333 = 0.00000 0.00000 + 84.33333333x + x2 = 0 + 46833.33333 84.33333333x + x2 = 0 + 46833.33333 Combine like terms: 0 + 46833.33333 = 46833.33333 84.33333333x + x2 = 46833.33333 The x term is 84.33333333x. Take half its coefficient (42.16666667). Square it (1778.027778) and add it to both sides. Add '1778.027778' to each side of the equation. 84.33333333x + 1778.027778 + x2 = 46833.33333 + 1778.027778 Reorder the terms: 1778.027778 + 84.33333333x + x2 = 46833.33333 + 1778.027778 Combine like terms: 46833.33333 + 1778.027778 = 48611.361108 1778.027778 + 84.33333333x + x2 = 48611.361108 Factor a perfect square on the left side: (x + 42.16666667)(x + 42.16666667) = 48611.361108 Calculate the square root of the right side: 220.479842861 Break this problem into two subproblems by setting (x + 42.16666667) equal to 220.479842861 and -220.479842861.Subproblem 1
x + 42.16666667 = 220.479842861 Simplifying x + 42.16666667 = 220.479842861 Reorder the terms: 42.16666667 + x = 220.479842861 Solving 42.16666667 + x = 220.479842861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.16666667' to each side of the equation. 42.16666667 + -42.16666667 + x = 220.479842861 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = 220.479842861 + -42.16666667 x = 220.479842861 + -42.16666667 Combine like terms: 220.479842861 + -42.16666667 = 178.313176191 x = 178.313176191 Simplifying x = 178.313176191Subproblem 2
x + 42.16666667 = -220.479842861 Simplifying x + 42.16666667 = -220.479842861 Reorder the terms: 42.16666667 + x = -220.479842861 Solving 42.16666667 + x = -220.479842861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.16666667' to each side of the equation. 42.16666667 + -42.16666667 + x = -220.479842861 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = -220.479842861 + -42.16666667 x = -220.479842861 + -42.16666667 Combine like terms: -220.479842861 + -42.16666667 = -262.646509531 x = -262.646509531 Simplifying x = -262.646509531Solution
The solution to the problem is based on the solutions from the subproblems. x = {178.313176191, -262.646509531}
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