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Simplifying 14x2 + 17x + -19 = 0 Reorder the terms: -19 + 17x + 14x2 = 0 Solving -19 + 17x + 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'. -1.357142857 + 1.214285714x + x2 = 0 Move the constant term to the right: Add '1.357142857' to each side of the equation. -1.357142857 + 1.214285714x + 1.357142857 + x2 = 0 + 1.357142857 Reorder the terms: -1.357142857 + 1.357142857 + 1.214285714x + x2 = 0 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + 1.214285714x + x2 = 0 + 1.357142857 1.214285714x + x2 = 0 + 1.357142857 Combine like terms: 0 + 1.357142857 = 1.357142857 1.214285714x + x2 = 1.357142857 The x term is 1.214285714x. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714x + 0.3686224488 + x2 = 1.357142857 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714x + x2 = 1.357142857 + 0.3686224488 Combine like terms: 1.357142857 + 0.3686224488 = 1.7257653058 0.3686224488 + 1.214285714x + x2 = 1.7257653058 Factor a perfect square on the left side: (x + 0.607142857)(x + 0.607142857) = 1.7257653058 Calculate the square root of the right side: 1.313683868 Break this problem into two subproblems by setting (x + 0.607142857) equal to 1.313683868 and -1.313683868.Subproblem 1
x + 0.607142857 = 1.313683868 Simplifying x + 0.607142857 = 1.313683868 Reorder the terms: 0.607142857 + x = 1.313683868 Solving 0.607142857 + x = 1.313683868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = 1.313683868 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = 1.313683868 + -0.607142857 x = 1.313683868 + -0.607142857 Combine like terms: 1.313683868 + -0.607142857 = 0.706541011 x = 0.706541011 Simplifying x = 0.706541011Subproblem 2
x + 0.607142857 = -1.313683868 Simplifying x + 0.607142857 = -1.313683868 Reorder the terms: 0.607142857 + x = -1.313683868 Solving 0.607142857 + x = -1.313683868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = -1.313683868 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = -1.313683868 + -0.607142857 x = -1.313683868 + -0.607142857 Combine like terms: -1.313683868 + -0.607142857 = -1.920826725 x = -1.920826725 Simplifying x = -1.920826725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.706541011, -1.920826725}
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