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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 = 609.9385632 367.2981691 + 38.33004926x + x2 = 609.9385632 Factor a perfect square on the left side: (x + 19.16502463)(x + 19.16502463) = 609.9385632 Calculate the square root of the right side: 24.696934287 Break this problem into two subproblems by setting (x + 19.16502463) equal to 24.696934287 and -24.696934287.Subproblem 1
x + 19.16502463 = 24.696934287 Simplifying x + 19.16502463 = 24.696934287 Reorder the terms: 19.16502463 + x = 24.696934287 Solving 19.16502463 + x = 24.696934287 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 = 24.696934287 + -19.16502463 Combine like terms: 19.16502463 + -19.16502463 = 0.00000000 0.00000000 + x = 24.696934287 + -19.16502463 x = 24.696934287 + -19.16502463 Combine like terms: 24.696934287 + -19.16502463 = 5.531909657 x = 5.531909657 Simplifying x = 5.531909657Subproblem 2
x + 19.16502463 = -24.696934287 Simplifying x + 19.16502463 = -24.696934287 Reorder the terms: 19.16502463 + x = -24.696934287 Solving 19.16502463 + x = -24.696934287 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 = -24.696934287 + -19.16502463 Combine like terms: 19.16502463 + -19.16502463 = 0.00000000 0.00000000 + x = -24.696934287 + -19.16502463 x = -24.696934287 + -19.16502463 Combine like terms: -24.696934287 + -19.16502463 = -43.861958917 x = -43.861958917 Simplifying x = -43.861958917Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.531909657, -43.861958917}
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