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Simplifying 140x2 + -36x + -15 = 0 Reorder the terms: -15 + -36x + 140x2 = 0 Solving -15 + -36x + 140x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 140 the coefficient of the squared term: Divide each side by '140'. -0.1071428571 + -0.2571428571x + x2 = 0 Move the constant term to the right: Add '0.1071428571' to each side of the equation. -0.1071428571 + -0.2571428571x + 0.1071428571 + x2 = 0 + 0.1071428571 Reorder the terms: -0.1071428571 + 0.1071428571 + -0.2571428571x + x2 = 0 + 0.1071428571 Combine like terms: -0.1071428571 + 0.1071428571 = 0.0000000000 0.0000000000 + -0.2571428571x + x2 = 0 + 0.1071428571 -0.2571428571x + x2 = 0 + 0.1071428571 Combine like terms: 0 + 0.1071428571 = 0.1071428571 -0.2571428571x + x2 = 0.1071428571 The x term is -0.2571428571x. Take half its coefficient (-0.1285714286). Square it (0.01653061225) and add it to both sides. Add '0.01653061225' to each side of the equation. -0.2571428571x + 0.01653061225 + x2 = 0.1071428571 + 0.01653061225 Reorder the terms: 0.01653061225 + -0.2571428571x + x2 = 0.1071428571 + 0.01653061225 Combine like terms: 0.1071428571 + 0.01653061225 = 0.12367346935 0.01653061225 + -0.2571428571x + x2 = 0.12367346935 Factor a perfect square on the left side: (x + -0.1285714286)(x + -0.1285714286) = 0.12367346935 Calculate the square root of the right side: 0.351672389 Break this problem into two subproblems by setting (x + -0.1285714286) equal to 0.351672389 and -0.351672389.Subproblem 1
x + -0.1285714286 = 0.351672389 Simplifying x + -0.1285714286 = 0.351672389 Reorder the terms: -0.1285714286 + x = 0.351672389 Solving -0.1285714286 + x = 0.351672389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1285714286' to each side of the equation. -0.1285714286 + 0.1285714286 + x = 0.351672389 + 0.1285714286 Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000 0.0000000000 + x = 0.351672389 + 0.1285714286 x = 0.351672389 + 0.1285714286 Combine like terms: 0.351672389 + 0.1285714286 = 0.4802438176 x = 0.4802438176 Simplifying x = 0.4802438176Subproblem 2
x + -0.1285714286 = -0.351672389 Simplifying x + -0.1285714286 = -0.351672389 Reorder the terms: -0.1285714286 + x = -0.351672389 Solving -0.1285714286 + x = -0.351672389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1285714286' to each side of the equation. -0.1285714286 + 0.1285714286 + x = -0.351672389 + 0.1285714286 Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000 0.0000000000 + x = -0.351672389 + 0.1285714286 x = -0.351672389 + 0.1285714286 Combine like terms: -0.351672389 + 0.1285714286 = -0.2231009604 x = -0.2231009604 Simplifying x = -0.2231009604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4802438176, -0.2231009604}
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