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Simplifying 0.0012x2 + -0.593x + 35.721 = 50 Reorder the terms: 35.721 + -0.593x + 0.0012x2 = 50 Solving 35.721 + -0.593x + 0.0012x2 = 50 Solving for variable 'x'. Reorder the terms: 35.721 + -50 + -0.593x + 0.0012x2 = 50 + -50 Combine like terms: 35.721 + -50 = -14.279 -14.279 + -0.593x + 0.0012x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -14.279 + -0.593x + 0.0012x2 = 0 Begin completing the square. Divide all terms by 0.0012 the coefficient of the squared term: Divide each side by '0.0012'. -11899.16667 + -494.1666667x + x2 = 0 Move the constant term to the right: Add '11899.16667' to each side of the equation. -11899.16667 + -494.1666667x + 11899.16667 + x2 = 0 + 11899.16667 Reorder the terms: -11899.16667 + 11899.16667 + -494.1666667x + x2 = 0 + 11899.16667 Combine like terms: -11899.16667 + 11899.16667 = 0.00000 0.00000 + -494.1666667x + x2 = 0 + 11899.16667 -494.1666667x + x2 = 0 + 11899.16667 Combine like terms: 0 + 11899.16667 = 11899.16667 -494.1666667x + x2 = 11899.16667 The x term is -494.1666667x. Take half its coefficient (-247.0833334). Square it (61050.17364) and add it to both sides. Add '61050.17364' to each side of the equation. -494.1666667x + 61050.17364 + x2 = 11899.16667 + 61050.17364 Reorder the terms: 61050.17364 + -494.1666667x + x2 = 11899.16667 + 61050.17364 Combine like terms: 11899.16667 + 61050.17364 = 72949.34031 61050.17364 + -494.1666667x + x2 = 72949.34031 Factor a perfect square on the left side: (x + -247.0833334)(x + -247.0833334) = 72949.34031 Calculate the square root of the right side: 270.091355489 Break this problem into two subproblems by setting (x + -247.0833334) equal to 270.091355489 and -270.091355489.Subproblem 1
x + -247.0833334 = 270.091355489 Simplifying x + -247.0833334 = 270.091355489 Reorder the terms: -247.0833334 + x = 270.091355489 Solving -247.0833334 + x = 270.091355489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '247.0833334' to each side of the equation. -247.0833334 + 247.0833334 + x = 270.091355489 + 247.0833334 Combine like terms: -247.0833334 + 247.0833334 = 0.0000000 0.0000000 + x = 270.091355489 + 247.0833334 x = 270.091355489 + 247.0833334 Combine like terms: 270.091355489 + 247.0833334 = 517.174688889 x = 517.174688889 Simplifying x = 517.174688889Subproblem 2
x + -247.0833334 = -270.091355489 Simplifying x + -247.0833334 = -270.091355489 Reorder the terms: -247.0833334 + x = -270.091355489 Solving -247.0833334 + x = -270.091355489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '247.0833334' to each side of the equation. -247.0833334 + 247.0833334 + x = -270.091355489 + 247.0833334 Combine like terms: -247.0833334 + 247.0833334 = 0.0000000 0.0000000 + x = -270.091355489 + 247.0833334 x = -270.091355489 + 247.0833334 Combine like terms: -270.091355489 + 247.0833334 = -23.008022089 x = -23.008022089 Simplifying x = -23.008022089Solution
The solution to the problem is based on the solutions from the subproblems. x = {517.174688889, -23.008022089}
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