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Simplifying 125x2 + -167x + 36 = 0 Reorder the terms: 36 + -167x + 125x2 = 0 Solving 36 + -167x + 125x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 125 the coefficient of the squared term: Divide each side by '125'. 0.288 + -1.336x + x2 = 0 Move the constant term to the right: Add '-0.288' to each side of the equation. 0.288 + -1.336x + -0.288 + x2 = 0 + -0.288 Reorder the terms: 0.288 + -0.288 + -1.336x + x2 = 0 + -0.288 Combine like terms: 0.288 + -0.288 = 0.000 0.000 + -1.336x + x2 = 0 + -0.288 -1.336x + x2 = 0 + -0.288 Combine like terms: 0 + -0.288 = -0.288 -1.336x + x2 = -0.288 The x term is -1.336x. Take half its coefficient (-0.668). Square it (0.446224) and add it to both sides. Add '0.446224' to each side of the equation. -1.336x + 0.446224 + x2 = -0.288 + 0.446224 Reorder the terms: 0.446224 + -1.336x + x2 = -0.288 + 0.446224 Combine like terms: -0.288 + 0.446224 = 0.158224 0.446224 + -1.336x + x2 = 0.158224 Factor a perfect square on the left side: (x + -0.668)(x + -0.668) = 0.158224 Calculate the square root of the right side: 0.397773805 Break this problem into two subproblems by setting (x + -0.668) equal to 0.397773805 and -0.397773805.Subproblem 1
x + -0.668 = 0.397773805 Simplifying x + -0.668 = 0.397773805 Reorder the terms: -0.668 + x = 0.397773805 Solving -0.668 + x = 0.397773805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.668' to each side of the equation. -0.668 + 0.668 + x = 0.397773805 + 0.668 Combine like terms: -0.668 + 0.668 = 0.000 0.000 + x = 0.397773805 + 0.668 x = 0.397773805 + 0.668 Combine like terms: 0.397773805 + 0.668 = 1.065773805 x = 1.065773805 Simplifying x = 1.065773805Subproblem 2
x + -0.668 = -0.397773805 Simplifying x + -0.668 = -0.397773805 Reorder the terms: -0.668 + x = -0.397773805 Solving -0.668 + x = -0.397773805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.668' to each side of the equation. -0.668 + 0.668 + x = -0.397773805 + 0.668 Combine like terms: -0.668 + 0.668 = 0.000 0.000 + x = -0.397773805 + 0.668 x = -0.397773805 + 0.668 Combine like terms: -0.397773805 + 0.668 = 0.270226195 x = 0.270226195 Simplifying x = 0.270226195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.065773805, 0.270226195}
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