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Simplifying 35x2 + -73x + -36 = 0 Reorder the terms: -36 + -73x + 35x2 = 0 Solving -36 + -73x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.028571429 + -2.085714286x + x2 = 0 Move the constant term to the right: Add '1.028571429' to each side of the equation. -1.028571429 + -2.085714286x + 1.028571429 + x2 = 0 + 1.028571429 Reorder the terms: -1.028571429 + 1.028571429 + -2.085714286x + x2 = 0 + 1.028571429 Combine like terms: -1.028571429 + 1.028571429 = 0.000000000 0.000000000 + -2.085714286x + x2 = 0 + 1.028571429 -2.085714286x + x2 = 0 + 1.028571429 Combine like terms: 0 + 1.028571429 = 1.028571429 -2.085714286x + x2 = 1.028571429 The x term is -2.085714286x. Take half its coefficient (-1.042857143). Square it (1.087551021) and add it to both sides. Add '1.087551021' to each side of the equation. -2.085714286x + 1.087551021 + x2 = 1.028571429 + 1.087551021 Reorder the terms: 1.087551021 + -2.085714286x + x2 = 1.028571429 + 1.087551021 Combine like terms: 1.028571429 + 1.087551021 = 2.11612245 1.087551021 + -2.085714286x + x2 = 2.11612245 Factor a perfect square on the left side: (x + -1.042857143)(x + -1.042857143) = 2.11612245 Calculate the square root of the right side: 1.454689812 Break this problem into two subproblems by setting (x + -1.042857143) equal to 1.454689812 and -1.454689812.Subproblem 1
x + -1.042857143 = 1.454689812 Simplifying x + -1.042857143 = 1.454689812 Reorder the terms: -1.042857143 + x = 1.454689812 Solving -1.042857143 + x = 1.454689812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.042857143' to each side of the equation. -1.042857143 + 1.042857143 + x = 1.454689812 + 1.042857143 Combine like terms: -1.042857143 + 1.042857143 = 0.000000000 0.000000000 + x = 1.454689812 + 1.042857143 x = 1.454689812 + 1.042857143 Combine like terms: 1.454689812 + 1.042857143 = 2.497546955 x = 2.497546955 Simplifying x = 2.497546955Subproblem 2
x + -1.042857143 = -1.454689812 Simplifying x + -1.042857143 = -1.454689812 Reorder the terms: -1.042857143 + x = -1.454689812 Solving -1.042857143 + x = -1.454689812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.042857143' to each side of the equation. -1.042857143 + 1.042857143 + x = -1.454689812 + 1.042857143 Combine like terms: -1.042857143 + 1.042857143 = 0.000000000 0.000000000 + x = -1.454689812 + 1.042857143 x = -1.454689812 + 1.042857143 Combine like terms: -1.454689812 + 1.042857143 = -0.411832669 x = -0.411832669 Simplifying x = -0.411832669Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.497546955, -0.411832669}
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