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Simplifying 3362.1x2 + -17270x + 24043 = 450000 Reorder the terms: 24043 + -17270x + 3362.1x2 = 450000 Solving 24043 + -17270x + 3362.1x2 = 450000 Solving for variable 'x'. Reorder the terms: 24043 + -450000 + -17270x + 3362.1x2 = 450000 + -450000 Combine like terms: 24043 + -450000 = -425957 -425957 + -17270x + 3362.1x2 = 450000 + -450000 Combine like terms: 450000 + -450000 = 0 -425957 + -17270x + 3362.1x2 = 0 Begin completing the square. Divide all terms by 3362.1 the coefficient of the squared term: Divide each side by '3362.1'. -126.6937331 + -5.136670533x + x2 = 0 Move the constant term to the right: Add '126.6937331' to each side of the equation. -126.6937331 + -5.136670533x + 126.6937331 + x2 = 0 + 126.6937331 Reorder the terms: -126.6937331 + 126.6937331 + -5.136670533x + x2 = 0 + 126.6937331 Combine like terms: -126.6937331 + 126.6937331 = 0.0000000 0.0000000 + -5.136670533x + x2 = 0 + 126.6937331 -5.136670533x + x2 = 0 + 126.6937331 Combine like terms: 0 + 126.6937331 = 126.6937331 -5.136670533x + x2 = 126.6937331 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 = 126.6937331 + 6.596346044 Reorder the terms: 6.596346044 + -5.136670533x + x2 = 126.6937331 + 6.596346044 Combine like terms: 126.6937331 + 6.596346044 = 133.290079144 6.596346044 + -5.136670533x + x2 = 133.290079144 Factor a perfect square on the left side: (x + -2.568335267)(x + -2.568335267) = 133.290079144 Calculate the square root of the right side: 11.545132271 Break this problem into two subproblems by setting (x + -2.568335267) equal to 11.545132271 and -11.545132271.Subproblem 1
x + -2.568335267 = 11.545132271 Simplifying x + -2.568335267 = 11.545132271 Reorder the terms: -2.568335267 + x = 11.545132271 Solving -2.568335267 + x = 11.545132271 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 = 11.545132271 + 2.568335267 Combine like terms: -2.568335267 + 2.568335267 = 0.000000000 0.000000000 + x = 11.545132271 + 2.568335267 x = 11.545132271 + 2.568335267 Combine like terms: 11.545132271 + 2.568335267 = 14.113467538 x = 14.113467538 Simplifying x = 14.113467538Subproblem 2
x + -2.568335267 = -11.545132271 Simplifying x + -2.568335267 = -11.545132271 Reorder the terms: -2.568335267 + x = -11.545132271 Solving -2.568335267 + x = -11.545132271 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 = -11.545132271 + 2.568335267 Combine like terms: -2.568335267 + 2.568335267 = 0.000000000 0.000000000 + x = -11.545132271 + 2.568335267 x = -11.545132271 + 2.568335267 Combine like terms: -11.545132271 + 2.568335267 = -8.976797004 x = -8.976797004 Simplifying x = -8.976797004Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.113467538, -8.976797004}
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