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Simplifying 14x2 + 15x + -13920 = 0 Reorder the terms: -13920 + 15x + 14x2 = 0 Solving -13920 + 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'. -994.2857143 + 1.071428571x + x2 = 0 Move the constant term to the right: Add '994.2857143' to each side of the equation. -994.2857143 + 1.071428571x + 994.2857143 + x2 = 0 + 994.2857143 Reorder the terms: -994.2857143 + 994.2857143 + 1.071428571x + x2 = 0 + 994.2857143 Combine like terms: -994.2857143 + 994.2857143 = 0.0000000 0.0000000 + 1.071428571x + x2 = 0 + 994.2857143 1.071428571x + x2 = 0 + 994.2857143 Combine like terms: 0 + 994.2857143 = 994.2857143 1.071428571x + x2 = 994.2857143 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 = 994.2857143 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571x + x2 = 994.2857143 + 0.2869897957 Combine like terms: 994.2857143 + 0.2869897957 = 994.5727040957 0.2869897957 + 1.071428571x + x2 = 994.5727040957 Factor a perfect square on the left side: (x + 0.5357142855)(x + 0.5357142855) = 994.5727040957 Calculate the square root of the right side: 31.536846768 Break this problem into two subproblems by setting (x + 0.5357142855) equal to 31.536846768 and -31.536846768.Subproblem 1
x + 0.5357142855 = 31.536846768 Simplifying x + 0.5357142855 = 31.536846768 Reorder the terms: 0.5357142855 + x = 31.536846768 Solving 0.5357142855 + x = 31.536846768 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 = 31.536846768 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = 31.536846768 + -0.5357142855 x = 31.536846768 + -0.5357142855 Combine like terms: 31.536846768 + -0.5357142855 = 31.0011324825 x = 31.0011324825 Simplifying x = 31.0011324825Subproblem 2
x + 0.5357142855 = -31.536846768 Simplifying x + 0.5357142855 = -31.536846768 Reorder the terms: 0.5357142855 + x = -31.536846768 Solving 0.5357142855 + x = -31.536846768 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 = -31.536846768 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = -31.536846768 + -0.5357142855 x = -31.536846768 + -0.5357142855 Combine like terms: -31.536846768 + -0.5357142855 = -32.0725610535 x = -32.0725610535 Simplifying x = -32.0725610535Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.0011324825, -32.0725610535}
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