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Simplifying x2 + 737.2x + 0.76 = 0 Reorder the terms: 0.76 + 737.2x + x2 = 0 Solving 0.76 + 737.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.76' to each side of the equation. 0.76 + 737.2x + -0.76 + x2 = 0 + -0.76 Reorder the terms: 0.76 + -0.76 + 737.2x + x2 = 0 + -0.76 Combine like terms: 0.76 + -0.76 = 0.00 0.00 + 737.2x + x2 = 0 + -0.76 737.2x + x2 = 0 + -0.76 Combine like terms: 0 + -0.76 = -0.76 737.2x + x2 = -0.76 The x term is 737.2x. Take half its coefficient (368.6). Square it (135865.96) and add it to both sides. Add '135865.96' to each side of the equation. 737.2x + 135865.96 + x2 = -0.76 + 135865.96 Reorder the terms: 135865.96 + 737.2x + x2 = -0.76 + 135865.96 Combine like terms: -0.76 + 135865.96 = 135865.2 135865.96 + 737.2x + x2 = 135865.2 Factor a perfect square on the left side: (x + 368.6)(x + 368.6) = 135865.2 Calculate the square root of the right side: 368.598969071 Break this problem into two subproblems by setting (x + 368.6) equal to 368.598969071 and -368.598969071.Subproblem 1
x + 368.6 = 368.598969071 Simplifying x + 368.6 = 368.598969071 Reorder the terms: 368.6 + x = 368.598969071 Solving 368.6 + x = 368.598969071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-368.6' to each side of the equation. 368.6 + -368.6 + x = 368.598969071 + -368.6 Combine like terms: 368.6 + -368.6 = 0.0 0.0 + x = 368.598969071 + -368.6 x = 368.598969071 + -368.6 Combine like terms: 368.598969071 + -368.6 = -0.001030929 x = -0.001030929 Simplifying x = -0.001030929Subproblem 2
x + 368.6 = -368.598969071 Simplifying x + 368.6 = -368.598969071 Reorder the terms: 368.6 + x = -368.598969071 Solving 368.6 + x = -368.598969071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-368.6' to each side of the equation. 368.6 + -368.6 + x = -368.598969071 + -368.6 Combine like terms: 368.6 + -368.6 = 0.0 0.0 + x = -368.598969071 + -368.6 x = -368.598969071 + -368.6 Combine like terms: -368.598969071 + -368.6 = -737.198969071 x = -737.198969071 Simplifying x = -737.198969071Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.001030929, -737.198969071}
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