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Simplifying 0 = -10.4x2 + 132x + -418 Reorder the terms: 0 = -418 + 132x + -10.4x2 Solving 0 = -418 + 132x + -10.4x2 Solving for variable 'x'. Combine like terms: 0 + 418 = 418 418 + -132x + 10.4x2 = -418 + 132x + -10.4x2 + 418 + -132x + 10.4x2 Reorder the terms: 418 + -132x + 10.4x2 = -418 + 418 + 132x + -132x + -10.4x2 + 10.4x2 Combine like terms: -418 + 418 = 0 418 + -132x + 10.4x2 = 0 + 132x + -132x + -10.4x2 + 10.4x2 418 + -132x + 10.4x2 = 132x + -132x + -10.4x2 + 10.4x2 Combine like terms: 132x + -132x = 0 418 + -132x + 10.4x2 = 0 + -10.4x2 + 10.4x2 418 + -132x + 10.4x2 = -10.4x2 + 10.4x2 Combine like terms: -10.4x2 + 10.4x2 = 0.0 418 + -132x + 10.4x2 = 0.0 Begin completing the square. Divide all terms by 10.4 the coefficient of the squared term: Divide each side by '10.4'. 40.19230769 + -12.69230769x + x2 = 0 Move the constant term to the right: Add '-40.19230769' to each side of the equation. 40.19230769 + -12.69230769x + -40.19230769 + x2 = 0 + -40.19230769 Reorder the terms: 40.19230769 + -40.19230769 + -12.69230769x + x2 = 0 + -40.19230769 Combine like terms: 40.19230769 + -40.19230769 = 0.00000000 0.00000000 + -12.69230769x + x2 = 0 + -40.19230769 -12.69230769x + x2 = 0 + -40.19230769 Combine like terms: 0 + -40.19230769 = -40.19230769 -12.69230769x + x2 = -40.19230769 The x term is -12.69230769x. Take half its coefficient (-6.346153845). Square it (40.27366862) and add it to both sides. Add '40.27366862' to each side of the equation. -12.69230769x + 40.27366862 + x2 = -40.19230769 + 40.27366862 Reorder the terms: 40.27366862 + -12.69230769x + x2 = -40.19230769 + 40.27366862 Combine like terms: -40.19230769 + 40.27366862 = 0.08136093 40.27366862 + -12.69230769x + x2 = 0.08136093 Factor a perfect square on the left side: (x + -6.346153845)(x + -6.346153845) = 0.08136093 Calculate the square root of the right side: 0.285238374 Break this problem into two subproblems by setting (x + -6.346153845) equal to 0.285238374 and -0.285238374.Subproblem 1
x + -6.346153845 = 0.285238374 Simplifying x + -6.346153845 = 0.285238374 Reorder the terms: -6.346153845 + x = 0.285238374 Solving -6.346153845 + x = 0.285238374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.346153845' to each side of the equation. -6.346153845 + 6.346153845 + x = 0.285238374 + 6.346153845 Combine like terms: -6.346153845 + 6.346153845 = 0.000000000 0.000000000 + x = 0.285238374 + 6.346153845 x = 0.285238374 + 6.346153845 Combine like terms: 0.285238374 + 6.346153845 = 6.631392219 x = 6.631392219 Simplifying x = 6.631392219Subproblem 2
x + -6.346153845 = -0.285238374 Simplifying x + -6.346153845 = -0.285238374 Reorder the terms: -6.346153845 + x = -0.285238374 Solving -6.346153845 + x = -0.285238374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.346153845' to each side of the equation. -6.346153845 + 6.346153845 + x = -0.285238374 + 6.346153845 Combine like terms: -6.346153845 + 6.346153845 = 0.000000000 0.000000000 + x = -0.285238374 + 6.346153845 x = -0.285238374 + 6.346153845 Combine like terms: -0.285238374 + 6.346153845 = 6.060915471 x = 6.060915471 Simplifying x = 6.060915471Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.631392219, 6.060915471}
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