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Simplifying 476x2 + -1680x + 1325 = 0 Reorder the terms: 1325 + -1680x + 476x2 = 0 Solving 1325 + -1680x + 476x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 476 the coefficient of the squared term: Divide each side by '476'. 2.783613445 + -3.529411765x + x2 = 0 Move the constant term to the right: Add '-2.783613445' to each side of the equation. 2.783613445 + -3.529411765x + -2.783613445 + x2 = 0 + -2.783613445 Reorder the terms: 2.783613445 + -2.783613445 + -3.529411765x + x2 = 0 + -2.783613445 Combine like terms: 2.783613445 + -2.783613445 = 0.000000000 0.000000000 + -3.529411765x + x2 = 0 + -2.783613445 -3.529411765x + x2 = 0 + -2.783613445 Combine like terms: 0 + -2.783613445 = -2.783613445 -3.529411765x + x2 = -2.783613445 The x term is -3.529411765x. Take half its coefficient (-1.764705883). Square it (3.114186853) and add it to both sides. Add '3.114186853' to each side of the equation. -3.529411765x + 3.114186853 + x2 = -2.783613445 + 3.114186853 Reorder the terms: 3.114186853 + -3.529411765x + x2 = -2.783613445 + 3.114186853 Combine like terms: -2.783613445 + 3.114186853 = 0.330573408 3.114186853 + -3.529411765x + x2 = 0.330573408 Factor a perfect square on the left side: (x + -1.764705883)(x + -1.764705883) = 0.330573408 Calculate the square root of the right side: 0.574955136 Break this problem into two subproblems by setting (x + -1.764705883) equal to 0.574955136 and -0.574955136.Subproblem 1
x + -1.764705883 = 0.574955136 Simplifying x + -1.764705883 = 0.574955136 Reorder the terms: -1.764705883 + x = 0.574955136 Solving -1.764705883 + x = 0.574955136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.764705883' to each side of the equation. -1.764705883 + 1.764705883 + x = 0.574955136 + 1.764705883 Combine like terms: -1.764705883 + 1.764705883 = 0.000000000 0.000000000 + x = 0.574955136 + 1.764705883 x = 0.574955136 + 1.764705883 Combine like terms: 0.574955136 + 1.764705883 = 2.339661019 x = 2.339661019 Simplifying x = 2.339661019Subproblem 2
x + -1.764705883 = -0.574955136 Simplifying x + -1.764705883 = -0.574955136 Reorder the terms: -1.764705883 + x = -0.574955136 Solving -1.764705883 + x = -0.574955136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.764705883' to each side of the equation. -1.764705883 + 1.764705883 + x = -0.574955136 + 1.764705883 Combine like terms: -1.764705883 + 1.764705883 = 0.000000000 0.000000000 + x = -0.574955136 + 1.764705883 x = -0.574955136 + 1.764705883 Combine like terms: -0.574955136 + 1.764705883 = 1.189750747 x = 1.189750747 Simplifying x = 1.189750747Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.339661019, 1.189750747}
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