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Simplifying -73x2 + 44750x + -5040 = 0 Reorder the terms: -5040 + 44750x + -73x2 = 0 Solving -5040 + 44750x + -73x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -73 the coefficient of the squared term: Divide each side by '-73'. 69.04109589 + -613.0136986x + x2 = 0 Move the constant term to the right: Add '-69.04109589' to each side of the equation. 69.04109589 + -613.0136986x + -69.04109589 + x2 = 0 + -69.04109589 Reorder the terms: 69.04109589 + -69.04109589 + -613.0136986x + x2 = 0 + -69.04109589 Combine like terms: 69.04109589 + -69.04109589 = 0.00000000 0.00000000 + -613.0136986x + x2 = 0 + -69.04109589 -613.0136986x + x2 = 0 + -69.04109589 Combine like terms: 0 + -69.04109589 = -69.04109589 -613.0136986x + x2 = -69.04109589 The x term is -613.0136986x. Take half its coefficient (-306.5068493). Square it (93946.44867) and add it to both sides. Add '93946.44867' to each side of the equation. -613.0136986x + 93946.44867 + x2 = -69.04109589 + 93946.44867 Reorder the terms: 93946.44867 + -613.0136986x + x2 = -69.04109589 + 93946.44867 Combine like terms: -69.04109589 + 93946.44867 = 93877.40757411 93946.44867 + -613.0136986x + x2 = 93877.40757411 Factor a perfect square on the left side: (x + -306.5068493)(x + -306.5068493) = 93877.40757411 Calculate the square root of the right side: 306.394202906 Break this problem into two subproblems by setting (x + -306.5068493) equal to 306.394202906 and -306.394202906.Subproblem 1
x + -306.5068493 = 306.394202906 Simplifying x + -306.5068493 = 306.394202906 Reorder the terms: -306.5068493 + x = 306.394202906 Solving -306.5068493 + x = 306.394202906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '306.5068493' to each side of the equation. -306.5068493 + 306.5068493 + x = 306.394202906 + 306.5068493 Combine like terms: -306.5068493 + 306.5068493 = 0.0000000 0.0000000 + x = 306.394202906 + 306.5068493 x = 306.394202906 + 306.5068493 Combine like terms: 306.394202906 + 306.5068493 = 612.901052206 x = 612.901052206 Simplifying x = 612.901052206Subproblem 2
x + -306.5068493 = -306.394202906 Simplifying x + -306.5068493 = -306.394202906 Reorder the terms: -306.5068493 + x = -306.394202906 Solving -306.5068493 + x = -306.394202906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '306.5068493' to each side of the equation. -306.5068493 + 306.5068493 + x = -306.394202906 + 306.5068493 Combine like terms: -306.5068493 + 306.5068493 = 0.0000000 0.0000000 + x = -306.394202906 + 306.5068493 x = -306.394202906 + 306.5068493 Combine like terms: -306.394202906 + 306.5068493 = 0.112646394 x = 0.112646394 Simplifying x = 0.112646394Solution
The solution to the problem is based on the solutions from the subproblems. x = {612.901052206, 0.112646394}
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