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Simplifying 14x2 + 15x + -4 = 0 Reorder the terms: -4 + 15x + 14x2 = 0 Solving -4 + 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'. -0.2857142857 + 1.071428571x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.071428571x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.071428571x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.071428571x + x2 = 0 + 0.2857142857 1.071428571x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.071428571x + x2 = 0.2857142857 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 = 0.2857142857 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571x + x2 = 0.2857142857 + 0.2869897957 Combine like terms: 0.2857142857 + 0.2869897957 = 0.5727040814 0.2869897957 + 1.071428571x + x2 = 0.5727040814 Factor a perfect square on the left side: (x + 0.5357142855)(x + 0.5357142855) = 0.5727040814 Calculate the square root of the right side: 0.756772146 Break this problem into two subproblems by setting (x + 0.5357142855) equal to 0.756772146 and -0.756772146.Subproblem 1
x + 0.5357142855 = 0.756772146 Simplifying x + 0.5357142855 = 0.756772146 Reorder the terms: 0.5357142855 + x = 0.756772146 Solving 0.5357142855 + x = 0.756772146 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 = 0.756772146 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = 0.756772146 + -0.5357142855 x = 0.756772146 + -0.5357142855 Combine like terms: 0.756772146 + -0.5357142855 = 0.2210578605 x = 0.2210578605 Simplifying x = 0.2210578605Subproblem 2
x + 0.5357142855 = -0.756772146 Simplifying x + 0.5357142855 = -0.756772146 Reorder the terms: 0.5357142855 + x = -0.756772146 Solving 0.5357142855 + x = -0.756772146 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 = -0.756772146 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = -0.756772146 + -0.5357142855 x = -0.756772146 + -0.5357142855 Combine like terms: -0.756772146 + -0.5357142855 = -1.2924864315 x = -1.2924864315 Simplifying x = -1.2924864315Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2210578605, -1.2924864315}
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