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Simplifying 550000 = 3362.1x2 + -17270x + 24043 Reorder the terms: 550000 = 24043 + -17270x + 3362.1x2 Solving 550000 = 24043 + -17270x + 3362.1x2 Solving for variable 'x'. Combine like terms: 550000 + -24043 = 525957 525957 + 17270x + -3362.1x2 = 24043 + -17270x + 3362.1x2 + -24043 + 17270x + -3362.1x2 Reorder the terms: 525957 + 17270x + -3362.1x2 = 24043 + -24043 + -17270x + 17270x + 3362.1x2 + -3362.1x2 Combine like terms: 24043 + -24043 = 0 525957 + 17270x + -3362.1x2 = 0 + -17270x + 17270x + 3362.1x2 + -3362.1x2 525957 + 17270x + -3362.1x2 = -17270x + 17270x + 3362.1x2 + -3362.1x2 Combine like terms: -17270x + 17270x = 0 525957 + 17270x + -3362.1x2 = 0 + 3362.1x2 + -3362.1x2 525957 + 17270x + -3362.1x2 = 3362.1x2 + -3362.1x2 Combine like terms: 3362.1x2 + -3362.1x2 = 0.0 525957 + 17270x + -3362.1x2 = 0.0 Begin completing the square. Divide all terms by -3362.1 the coefficient of the squared term: Divide each side by '-3362.1'. -156.4370483 + -5.136670533x + x2 = 0 Move the constant term to the right: Add '156.4370483' to each side of the equation. -156.4370483 + -5.136670533x + 156.4370483 + x2 = 0 + 156.4370483 Reorder the terms: -156.4370483 + 156.4370483 + -5.136670533x + x2 = 0 + 156.4370483 Combine like terms: -156.4370483 + 156.4370483 = 0.0000000 0.0000000 + -5.136670533x + x2 = 0 + 156.4370483 -5.136670533x + x2 = 0 + 156.4370483 Combine like terms: 0 + 156.4370483 = 156.4370483 -5.136670533x + x2 = 156.4370483 The x term is -5.136670533x. Take half its coefficient (-2.568335267). Square it (6.596346044) and add it to both sides. Add '6.596346044' to each side of the equation. -5.136670533x + 6.596346044 + x2 = 156.4370483 + 6.596346044 Reorder the terms: 6.596346044 + -5.136670533x + x2 = 156.4370483 + 6.596346044 Combine like terms: 156.4370483 + 6.596346044 = 163.033394344 6.596346044 + -5.136670533x + x2 = 163.033394344 Factor a perfect square on the left side: (x + -2.568335267)(x + -2.568335267) = 163.033394344 Calculate the square root of the right side: 12.768453091 Break this problem into two subproblems by setting (x + -2.568335267) equal to 12.768453091 and -12.768453091.Subproblem 1
x + -2.568335267 = 12.768453091 Simplifying x + -2.568335267 = 12.768453091 Reorder the terms: -2.568335267 + x = 12.768453091 Solving -2.568335267 + x = 12.768453091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.568335267' to each side of the equation. -2.568335267 + 2.568335267 + x = 12.768453091 + 2.568335267 Combine like terms: -2.568335267 + 2.568335267 = 0.000000000 0.000000000 + x = 12.768453091 + 2.568335267 x = 12.768453091 + 2.568335267 Combine like terms: 12.768453091 + 2.568335267 = 15.336788358 x = 15.336788358 Simplifying x = 15.336788358Subproblem 2
x + -2.568335267 = -12.768453091 Simplifying x + -2.568335267 = -12.768453091 Reorder the terms: -2.568335267 + x = -12.768453091 Solving -2.568335267 + x = -12.768453091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.568335267' to each side of the equation. -2.568335267 + 2.568335267 + x = -12.768453091 + 2.568335267 Combine like terms: -2.568335267 + 2.568335267 = 0.000000000 0.000000000 + x = -12.768453091 + 2.568335267 x = -12.768453091 + 2.568335267 Combine like terms: -12.768453091 + 2.568335267 = -10.200117824 x = -10.200117824 Simplifying x = -10.200117824Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.336788358, -10.200117824}
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