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Simplifying 4000000000 = 3.51x2 + 24.4x + 780 Reorder the terms: 4000000000 = 780 + 24.4x + 3.51x2 Solving 4000000000 = 780 + 24.4x + 3.51x2 Solving for variable 'x'. Combine like terms: 4000000000 + -780 = 3999999220 3999999220 + -24.4x + -3.51x2 = 780 + 24.4x + 3.51x2 + -780 + -24.4x + -3.51x2 Reorder the terms: 3999999220 + -24.4x + -3.51x2 = 780 + -780 + 24.4x + -24.4x + 3.51x2 + -3.51x2 Combine like terms: 780 + -780 = 0 3999999220 + -24.4x + -3.51x2 = 0 + 24.4x + -24.4x + 3.51x2 + -3.51x2 3999999220 + -24.4x + -3.51x2 = 24.4x + -24.4x + 3.51x2 + -3.51x2 Combine like terms: 24.4x + -24.4x = 0.0 3999999220 + -24.4x + -3.51x2 = 0.0 + 3.51x2 + -3.51x2 3999999220 + -24.4x + -3.51x2 = 3.51x2 + -3.51x2 Combine like terms: 3.51x2 + -3.51x2 = 0.00 3999999220 + -24.4x + -3.51x2 = 0.00 Begin completing the square. Divide all terms by -3.51 the coefficient of the squared term: Divide each side by '-3.51'. -1139600917 + 6.951566952x + x2 = 0 Move the constant term to the right: Add '1139600917' to each side of the equation. -1139600917 + 6.951566952x + 1139600917 + x2 = 0 + 1139600917 Reorder the terms: -1139600917 + 1139600917 + 6.951566952x + x2 = 0 + 1139600917 Combine like terms: -1139600917 + 1139600917 = 0 0 + 6.951566952x + x2 = 0 + 1139600917 6.951566952x + x2 = 0 + 1139600917 Combine like terms: 0 + 1139600917 = 1139600917 6.951566952x + x2 = 1139600917 The x term is 6.951566952x. Take half its coefficient (3.475783476). Square it (12.08107077) and add it to both sides. Add '12.08107077' to each side of the equation. 6.951566952x + 12.08107077 + x2 = 1139600917 + 12.08107077 Reorder the terms: 12.08107077 + 6.951566952x + x2 = 1139600917 + 12.08107077 Combine like terms: 1139600917 + 12.08107077 = 1139600929.08107077 12.08107077 + 6.951566952x + x2 = 1139600929.08107077 Factor a perfect square on the left side: (x + 3.475783476)(x + 3.475783476) = 1139600929.08107077 Calculate the square root of the right side: 33757.97578471 Break this problem into two subproblems by setting (x + 3.475783476) equal to 33757.97578471 and -33757.97578471.Subproblem 1
x + 3.475783476 = 33757.97578471 Simplifying x + 3.475783476 = 33757.97578471 Reorder the terms: 3.475783476 + x = 33757.97578471 Solving 3.475783476 + x = 33757.97578471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.475783476' to each side of the equation. 3.475783476 + -3.475783476 + x = 33757.97578471 + -3.475783476 Combine like terms: 3.475783476 + -3.475783476 = 0.000000000 0.000000000 + x = 33757.97578471 + -3.475783476 x = 33757.97578471 + -3.475783476 Combine like terms: 33757.97578471 + -3.475783476 = 33754.500001234 x = 33754.500001234 Simplifying x = 33754.500001234Subproblem 2
x + 3.475783476 = -33757.97578471 Simplifying x + 3.475783476 = -33757.97578471 Reorder the terms: 3.475783476 + x = -33757.97578471 Solving 3.475783476 + x = -33757.97578471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.475783476' to each side of the equation. 3.475783476 + -3.475783476 + x = -33757.97578471 + -3.475783476 Combine like terms: 3.475783476 + -3.475783476 = 0.000000000 0.000000000 + x = -33757.97578471 + -3.475783476 x = -33757.97578471 + -3.475783476 Combine like terms: -33757.97578471 + -3.475783476 = -33761.451568186 x = -33761.451568186 Simplifying x = -33761.451568186Solution
The solution to the problem is based on the solutions from the subproblems. x = {33754.500001234, -33761.451568186}
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