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Simplifying 40923x2 + -1132.53x + 40547.698 = 32713000 Reorder the terms: 40547.698 + -1132.53x + 40923x2 = 32713000 Solving 40547.698 + -1132.53x + 40923x2 = 32713000 Solving for variable 'x'. Reorder the terms: 40547.698 + -32713000 + -1132.53x + 40923x2 = 32713000 + -32713000 Combine like terms: 40547.698 + -32713000 = -32672452.302 -32672452.302 + -1132.53x + 40923x2 = 32713000 + -32713000 Combine like terms: 32713000 + -32713000 = 0 -32672452.302 + -1132.53x + 40923x2 = 0 Begin completing the square. Divide all terms by 40923 the coefficient of the squared term: Divide each side by '40923'. -798.3884931 + -0.02767465728x + x2 = 0 Move the constant term to the right: Add '798.3884931' to each side of the equation. -798.3884931 + -0.02767465728x + 798.3884931 + x2 = 0 + 798.3884931 Reorder the terms: -798.3884931 + 798.3884931 + -0.02767465728x + x2 = 0 + 798.3884931 Combine like terms: -798.3884931 + 798.3884931 = 0.0000000 0.0000000 + -0.02767465728x + x2 = 0 + 798.3884931 -0.02767465728x + x2 = 0 + 798.3884931 Combine like terms: 0 + 798.3884931 = 798.3884931 -0.02767465728x + x2 = 798.3884931 The x term is -0.02767465728x. Take half its coefficient (-0.01383732864). Square it (0.0001914716639) and add it to both sides. Add '0.0001914716639' to each side of the equation. -0.02767465728x + 0.0001914716639 + x2 = 798.3884931 + 0.0001914716639 Reorder the terms: 0.0001914716639 + -0.02767465728x + x2 = 798.3884931 + 0.0001914716639 Combine like terms: 798.3884931 + 0.0001914716639 = 798.3886845716639 0.0001914716639 + -0.02767465728x + x2 = 798.3886845716639 Factor a perfect square on the left side: (x + -0.01383732864)(x + -0.01383732864) = 798.3886845716639 Calculate the square root of the right side: 28.255772588 Break this problem into two subproblems by setting (x + -0.01383732864) equal to 28.255772588 and -28.255772588.Subproblem 1
x + -0.01383732864 = 28.255772588 Simplifying x + -0.01383732864 = 28.255772588 Reorder the terms: -0.01383732864 + x = 28.255772588 Solving -0.01383732864 + x = 28.255772588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01383732864' to each side of the equation. -0.01383732864 + 0.01383732864 + x = 28.255772588 + 0.01383732864 Combine like terms: -0.01383732864 + 0.01383732864 = 0.00000000000 0.00000000000 + x = 28.255772588 + 0.01383732864 x = 28.255772588 + 0.01383732864 Combine like terms: 28.255772588 + 0.01383732864 = 28.26960991664 x = 28.26960991664 Simplifying x = 28.26960991664Subproblem 2
x + -0.01383732864 = -28.255772588 Simplifying x + -0.01383732864 = -28.255772588 Reorder the terms: -0.01383732864 + x = -28.255772588 Solving -0.01383732864 + x = -28.255772588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01383732864' to each side of the equation. -0.01383732864 + 0.01383732864 + x = -28.255772588 + 0.01383732864 Combine like terms: -0.01383732864 + 0.01383732864 = 0.00000000000 0.00000000000 + x = -28.255772588 + 0.01383732864 x = -28.255772588 + 0.01383732864 Combine like terms: -28.255772588 + 0.01383732864 = -28.24193525936 x = -28.24193525936 Simplifying x = -28.24193525936Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.26960991664, -28.24193525936}
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