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Simplifying 14x2 + -8x + -25 = 0 Reorder the terms: -25 + -8x + 14x2 = 0 Solving -25 + -8x + 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 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.785714286' to each side of the equation. -1.785714286 + -0.5714285714x + 1.785714286 + x2 = 0 + 1.785714286 Reorder the terms: -1.785714286 + 1.785714286 + -0.5714285714x + x2 = 0 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 1.785714286 -0.5714285714x + x2 = 0 + 1.785714286 Combine like terms: 0 + 1.785714286 = 1.785714286 -0.5714285714x + x2 = 1.785714286 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 1.785714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 1.785714286 + 0.08163265305 Combine like terms: 1.785714286 + 0.08163265305 = 1.86734693905 0.08163265305 + -0.5714285714x + x2 = 1.86734693905 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 1.86734693905 Calculate the square root of the right side: 1.366509034 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.366509034 and -1.366509034.Subproblem 1
x + -0.2857142857 = 1.366509034 Simplifying x + -0.2857142857 = 1.366509034 Reorder the terms: -0.2857142857 + x = 1.366509034 Solving -0.2857142857 + x = 1.366509034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.366509034 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.366509034 + 0.2857142857 x = 1.366509034 + 0.2857142857 Combine like terms: 1.366509034 + 0.2857142857 = 1.6522233197 x = 1.6522233197 Simplifying x = 1.6522233197Subproblem 2
x + -0.2857142857 = -1.366509034 Simplifying x + -0.2857142857 = -1.366509034 Reorder the terms: -0.2857142857 + x = -1.366509034 Solving -0.2857142857 + x = -1.366509034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.366509034 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.366509034 + 0.2857142857 x = -1.366509034 + 0.2857142857 Combine like terms: -1.366509034 + 0.2857142857 = -1.0807947483 x = -1.0807947483 Simplifying x = -1.0807947483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6522233197, -1.0807947483}
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