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Simplifying 14x2 + -15x + -25 = 0 Reorder the terms: -25 + -15x + 14x2 = 0 Solving -25 + -15x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.785714286 + -1.071428571x + x2 = 0 Move the constant term to the right: Add '1.785714286' to each side of the equation. -1.785714286 + -1.071428571x + 1.785714286 + x2 = 0 + 1.785714286 Reorder the terms: -1.785714286 + 1.785714286 + -1.071428571x + x2 = 0 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + -1.071428571x + x2 = 0 + 1.785714286 -1.071428571x + x2 = 0 + 1.785714286 Combine like terms: 0 + 1.785714286 = 1.785714286 -1.071428571x + x2 = 1.785714286 The x term is -1.071428571x. Take half its coefficient (-0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. -1.071428571x + 0.2869897957 + x2 = 1.785714286 + 0.2869897957 Reorder the terms: 0.2869897957 + -1.071428571x + x2 = 1.785714286 + 0.2869897957 Combine like terms: 1.785714286 + 0.2869897957 = 2.0727040817 0.2869897957 + -1.071428571x + x2 = 2.0727040817 Factor a perfect square on the left side: (x + -0.5357142855)(x + -0.5357142855) = 2.0727040817 Calculate the square root of the right side: 1.439688884 Break this problem into two subproblems by setting (x + -0.5357142855) equal to 1.439688884 and -1.439688884.Subproblem 1
x + -0.5357142855 = 1.439688884 Simplifying x + -0.5357142855 = 1.439688884 Reorder the terms: -0.5357142855 + x = 1.439688884 Solving -0.5357142855 + x = 1.439688884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5357142855' to each side of the equation. -0.5357142855 + 0.5357142855 + x = 1.439688884 + 0.5357142855 Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000 0.0000000000 + x = 1.439688884 + 0.5357142855 x = 1.439688884 + 0.5357142855 Combine like terms: 1.439688884 + 0.5357142855 = 1.9754031695 x = 1.9754031695 Simplifying x = 1.9754031695Subproblem 2
x + -0.5357142855 = -1.439688884 Simplifying x + -0.5357142855 = -1.439688884 Reorder the terms: -0.5357142855 + x = -1.439688884 Solving -0.5357142855 + x = -1.439688884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5357142855' to each side of the equation. -0.5357142855 + 0.5357142855 + x = -1.439688884 + 0.5357142855 Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000 0.0000000000 + x = -1.439688884 + 0.5357142855 x = -1.439688884 + 0.5357142855 Combine like terms: -1.439688884 + 0.5357142855 = -0.9039745985 x = -0.9039745985 Simplifying x = -0.9039745985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9754031695, -0.9039745985}
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