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Simplifying 3x2 + 253x = 120000 Reorder the terms: 253x + 3x2 = 120000 Solving 253x + 3x2 = 120000 Solving for variable 'x'. Reorder the terms: -120000 + 253x + 3x2 = 120000 + -120000 Combine like terms: 120000 + -120000 = 0 -120000 + 253x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -40000 + 84.33333333x + x2 = 0 Move the constant term to the right: Add '40000' to each side of the equation. -40000 + 84.33333333x + 40000 + x2 = 0 + 40000 Reorder the terms: -40000 + 40000 + 84.33333333x + x2 = 0 + 40000 Combine like terms: -40000 + 40000 = 0 0 + 84.33333333x + x2 = 0 + 40000 84.33333333x + x2 = 0 + 40000 Combine like terms: 0 + 40000 = 40000 84.33333333x + x2 = 40000 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 = 40000 + 1778.027778 Reorder the terms: 1778.027778 + 84.33333333x + x2 = 40000 + 1778.027778 Combine like terms: 40000 + 1778.027778 = 41778.027778 1778.027778 + 84.33333333x + x2 = 41778.027778 Factor a perfect square on the left side: (x + 42.16666667)(x + 42.16666667) = 41778.027778 Calculate the square root of the right side: 204.396741114 Break this problem into two subproblems by setting (x + 42.16666667) equal to 204.396741114 and -204.396741114.Subproblem 1
x + 42.16666667 = 204.396741114 Simplifying x + 42.16666667 = 204.396741114 Reorder the terms: 42.16666667 + x = 204.396741114 Solving 42.16666667 + x = 204.396741114 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 = 204.396741114 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = 204.396741114 + -42.16666667 x = 204.396741114 + -42.16666667 Combine like terms: 204.396741114 + -42.16666667 = 162.230074444 x = 162.230074444 Simplifying x = 162.230074444Subproblem 2
x + 42.16666667 = -204.396741114 Simplifying x + 42.16666667 = -204.396741114 Reorder the terms: 42.16666667 + x = -204.396741114 Solving 42.16666667 + x = -204.396741114 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 = -204.396741114 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = -204.396741114 + -42.16666667 x = -204.396741114 + -42.16666667 Combine like terms: -204.396741114 + -42.16666667 = -246.563407784 x = -246.563407784 Simplifying x = -246.563407784Solution
The solution to the problem is based on the solutions from the subproblems. x = {162.230074444, -246.563407784}
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