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Simplifying 1239.56 = -2.03x2 + 77.81x + 747 Reorder the terms: 1239.56 = 747 + 77.81x + -2.03x2 Solving 1239.56 = 747 + 77.81x + -2.03x2 Solving for variable 'x'. Combine like terms: 1239.56 + -747 = 492.56 492.56 + -77.81x + 2.03x2 = 747 + 77.81x + -2.03x2 + -747 + -77.81x + 2.03x2 Reorder the terms: 492.56 + -77.81x + 2.03x2 = 747 + -747 + 77.81x + -77.81x + -2.03x2 + 2.03x2 Combine like terms: 747 + -747 = 0 492.56 + -77.81x + 2.03x2 = 0 + 77.81x + -77.81x + -2.03x2 + 2.03x2 492.56 + -77.81x + 2.03x2 = 77.81x + -77.81x + -2.03x2 + 2.03x2 Combine like terms: 77.81x + -77.81x = 0.00 492.56 + -77.81x + 2.03x2 = 0.00 + -2.03x2 + 2.03x2 492.56 + -77.81x + 2.03x2 = -2.03x2 + 2.03x2 Combine like terms: -2.03x2 + 2.03x2 = 0.00 492.56 + -77.81x + 2.03x2 = 0.00 Begin completing the square. Divide all terms by 2.03 the coefficient of the squared term: Divide each side by '2.03'. 242.6403941 + -38.33004926x + x2 = 0 Move the constant term to the right: Add '-242.6403941' to each side of the equation. 242.6403941 + -38.33004926x + -242.6403941 + x2 = 0 + -242.6403941 Reorder the terms: 242.6403941 + -242.6403941 + -38.33004926x + x2 = 0 + -242.6403941 Combine like terms: 242.6403941 + -242.6403941 = 0.0000000 0.0000000 + -38.33004926x + x2 = 0 + -242.6403941 -38.33004926x + x2 = 0 + -242.6403941 Combine like terms: 0 + -242.6403941 = -242.6403941 -38.33004926x + x2 = -242.6403941 The x term is -38.33004926x. Take half its coefficient (-19.16502463). Square it (367.2981691) and add it to both sides. Add '367.2981691' to each side of the equation. -38.33004926x + 367.2981691 + x2 = -242.6403941 + 367.2981691 Reorder the terms: 367.2981691 + -38.33004926x + x2 = -242.6403941 + 367.2981691 Combine like terms: -242.6403941 + 367.2981691 = 124.657775 367.2981691 + -38.33004926x + x2 = 124.657775 Factor a perfect square on the left side: (x + -19.16502463)(x + -19.16502463) = 124.657775 Calculate the square root of the right side: 11.165024631 Break this problem into two subproblems by setting (x + -19.16502463) equal to 11.165024631 and -11.165024631.Subproblem 1
x + -19.16502463 = 11.165024631 Simplifying x + -19.16502463 = 11.165024631 Reorder the terms: -19.16502463 + x = 11.165024631 Solving -19.16502463 + x = 11.165024631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.16502463' to each side of the equation. -19.16502463 + 19.16502463 + x = 11.165024631 + 19.16502463 Combine like terms: -19.16502463 + 19.16502463 = 0.00000000 0.00000000 + x = 11.165024631 + 19.16502463 x = 11.165024631 + 19.16502463 Combine like terms: 11.165024631 + 19.16502463 = 30.330049261 x = 30.330049261 Simplifying x = 30.330049261Subproblem 2
x + -19.16502463 = -11.165024631 Simplifying x + -19.16502463 = -11.165024631 Reorder the terms: -19.16502463 + x = -11.165024631 Solving -19.16502463 + x = -11.165024631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.16502463' to each side of the equation. -19.16502463 + 19.16502463 + x = -11.165024631 + 19.16502463 Combine like terms: -19.16502463 + 19.16502463 = 0.00000000 0.00000000 + x = -11.165024631 + 19.16502463 x = -11.165024631 + 19.16502463 Combine like terms: -11.165024631 + 19.16502463 = 7.999999999 x = 7.999999999 Simplifying x = 7.999999999Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.330049261, 7.999999999}
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