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Simplifying 5.38x2 + -10.14x + 3.77 = 0 Reorder the terms: 3.77 + -10.14x + 5.38x2 = 0 Solving 3.77 + -10.14x + 5.38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.38 the coefficient of the squared term: Divide each side by '5.38'. 0.7007434944 + -1.884758364x + x2 = 0 Move the constant term to the right: Add '-0.7007434944' to each side of the equation. 0.7007434944 + -1.884758364x + -0.7007434944 + x2 = 0 + -0.7007434944 Reorder the terms: 0.7007434944 + -0.7007434944 + -1.884758364x + x2 = 0 + -0.7007434944 Combine like terms: 0.7007434944 + -0.7007434944 = 0.0000000000 0.0000000000 + -1.884758364x + x2 = 0 + -0.7007434944 -1.884758364x + x2 = 0 + -0.7007434944 Combine like terms: 0 + -0.7007434944 = -0.7007434944 -1.884758364x + x2 = -0.7007434944 The x term is -1.884758364x. Take half its coefficient (-0.942379182). Square it (0.8880785227) and add it to both sides. Add '0.8880785227' to each side of the equation. -1.884758364x + 0.8880785227 + x2 = -0.7007434944 + 0.8880785227 Reorder the terms: 0.8880785227 + -1.884758364x + x2 = -0.7007434944 + 0.8880785227 Combine like terms: -0.7007434944 + 0.8880785227 = 0.1873350283 0.8880785227 + -1.884758364x + x2 = 0.1873350283 Factor a perfect square on the left side: (x + -0.942379182)(x + -0.942379182) = 0.1873350283 Calculate the square root of the right side: 0.432822167 Break this problem into two subproblems by setting (x + -0.942379182) equal to 0.432822167 and -0.432822167.Subproblem 1
x + -0.942379182 = 0.432822167 Simplifying x + -0.942379182 = 0.432822167 Reorder the terms: -0.942379182 + x = 0.432822167 Solving -0.942379182 + x = 0.432822167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.942379182' to each side of the equation. -0.942379182 + 0.942379182 + x = 0.432822167 + 0.942379182 Combine like terms: -0.942379182 + 0.942379182 = 0.000000000 0.000000000 + x = 0.432822167 + 0.942379182 x = 0.432822167 + 0.942379182 Combine like terms: 0.432822167 + 0.942379182 = 1.375201349 x = 1.375201349 Simplifying x = 1.375201349Subproblem 2
x + -0.942379182 = -0.432822167 Simplifying x + -0.942379182 = -0.432822167 Reorder the terms: -0.942379182 + x = -0.432822167 Solving -0.942379182 + x = -0.432822167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.942379182' to each side of the equation. -0.942379182 + 0.942379182 + x = -0.432822167 + 0.942379182 Combine like terms: -0.942379182 + 0.942379182 = 0.000000000 0.000000000 + x = -0.432822167 + 0.942379182 x = -0.432822167 + 0.942379182 Combine like terms: -0.432822167 + 0.942379182 = 0.509557015 x = 0.509557015 Simplifying x = 0.509557015Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.375201349, 0.509557015}
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