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Simplifying 9x2 + -125x + 80 = 0 Reorder the terms: 80 + -125x + 9x2 = 0 Solving 80 + -125x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.888888889 + -13.88888889x + x2 = 0 Move the constant term to the right: Add '-8.888888889' to each side of the equation. 8.888888889 + -13.88888889x + -8.888888889 + x2 = 0 + -8.888888889 Reorder the terms: 8.888888889 + -8.888888889 + -13.88888889x + x2 = 0 + -8.888888889 Combine like terms: 8.888888889 + -8.888888889 = 0.000000000 0.000000000 + -13.88888889x + x2 = 0 + -8.888888889 -13.88888889x + x2 = 0 + -8.888888889 Combine like terms: 0 + -8.888888889 = -8.888888889 -13.88888889x + x2 = -8.888888889 The x term is -13.88888889x. Take half its coefficient (-6.944444445). Square it (48.22530865) and add it to both sides. Add '48.22530865' to each side of the equation. -13.88888889x + 48.22530865 + x2 = -8.888888889 + 48.22530865 Reorder the terms: 48.22530865 + -13.88888889x + x2 = -8.888888889 + 48.22530865 Combine like terms: -8.888888889 + 48.22530865 = 39.336419761 48.22530865 + -13.88888889x + x2 = 39.336419761 Factor a perfect square on the left side: (x + -6.944444445)(x + -6.944444445) = 39.336419761 Calculate the square root of the right side: 6.271875299 Break this problem into two subproblems by setting (x + -6.944444445) equal to 6.271875299 and -6.271875299.Subproblem 1
x + -6.944444445 = 6.271875299 Simplifying x + -6.944444445 = 6.271875299 Reorder the terms: -6.944444445 + x = 6.271875299 Solving -6.944444445 + x = 6.271875299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.944444445' to each side of the equation. -6.944444445 + 6.944444445 + x = 6.271875299 + 6.944444445 Combine like terms: -6.944444445 + 6.944444445 = 0.000000000 0.000000000 + x = 6.271875299 + 6.944444445 x = 6.271875299 + 6.944444445 Combine like terms: 6.271875299 + 6.944444445 = 13.216319744 x = 13.216319744 Simplifying x = 13.216319744Subproblem 2
x + -6.944444445 = -6.271875299 Simplifying x + -6.944444445 = -6.271875299 Reorder the terms: -6.944444445 + x = -6.271875299 Solving -6.944444445 + x = -6.271875299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.944444445' to each side of the equation. -6.944444445 + 6.944444445 + x = -6.271875299 + 6.944444445 Combine like terms: -6.944444445 + 6.944444445 = 0.000000000 0.000000000 + x = -6.271875299 + 6.944444445 x = -6.271875299 + 6.944444445 Combine like terms: -6.271875299 + 6.944444445 = 0.672569146 x = 0.672569146 Simplifying x = 0.672569146Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.216319744, 0.672569146}
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