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Simplifying 169x2 + -356x + 144 = 0 Reorder the terms: 144 + -356x + 169x2 = 0 Solving 144 + -356x + 169x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 169 the coefficient of the squared term: Divide each side by '169'. 0.8520710059 + -2.106508876x + x2 = 0 Move the constant term to the right: Add '-0.8520710059' to each side of the equation. 0.8520710059 + -2.106508876x + -0.8520710059 + x2 = 0 + -0.8520710059 Reorder the terms: 0.8520710059 + -0.8520710059 + -2.106508876x + x2 = 0 + -0.8520710059 Combine like terms: 0.8520710059 + -0.8520710059 = 0.0000000000 0.0000000000 + -2.106508876x + x2 = 0 + -0.8520710059 -2.106508876x + x2 = 0 + -0.8520710059 Combine like terms: 0 + -0.8520710059 = -0.8520710059 -2.106508876x + x2 = -0.8520710059 The x term is -2.106508876x. Take half its coefficient (-1.053254438). Square it (1.109344911) and add it to both sides. Add '1.109344911' to each side of the equation. -2.106508876x + 1.109344911 + x2 = -0.8520710059 + 1.109344911 Reorder the terms: 1.109344911 + -2.106508876x + x2 = -0.8520710059 + 1.109344911 Combine like terms: -0.8520710059 + 1.109344911 = 0.2572739051 1.109344911 + -2.106508876x + x2 = 0.2572739051 Factor a perfect square on the left side: (x + -1.053254438)(x + -1.053254438) = 0.2572739051 Calculate the square root of the right side: 0.507221751 Break this problem into two subproblems by setting (x + -1.053254438) equal to 0.507221751 and -0.507221751.Subproblem 1
x + -1.053254438 = 0.507221751 Simplifying x + -1.053254438 = 0.507221751 Reorder the terms: -1.053254438 + x = 0.507221751 Solving -1.053254438 + x = 0.507221751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.053254438' to each side of the equation. -1.053254438 + 1.053254438 + x = 0.507221751 + 1.053254438 Combine like terms: -1.053254438 + 1.053254438 = 0.000000000 0.000000000 + x = 0.507221751 + 1.053254438 x = 0.507221751 + 1.053254438 Combine like terms: 0.507221751 + 1.053254438 = 1.560476189 x = 1.560476189 Simplifying x = 1.560476189Subproblem 2
x + -1.053254438 = -0.507221751 Simplifying x + -1.053254438 = -0.507221751 Reorder the terms: -1.053254438 + x = -0.507221751 Solving -1.053254438 + x = -0.507221751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.053254438' to each side of the equation. -1.053254438 + 1.053254438 + x = -0.507221751 + 1.053254438 Combine like terms: -1.053254438 + 1.053254438 = 0.000000000 0.000000000 + x = -0.507221751 + 1.053254438 x = -0.507221751 + 1.053254438 Combine like terms: -0.507221751 + 1.053254438 = 0.546032687 x = 0.546032687 Simplifying x = 0.546032687Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.560476189, 0.546032687}
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