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Simplifying 14x2 + 17x + -15 = 0 Reorder the terms: -15 + 17x + 14x2 = 0 Solving -15 + 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'. -1.071428571 + 1.214285714x + x2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + 1.214285714x + 1.071428571 + x2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + 1.214285714x + x2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + 1.214285714x + x2 = 0 + 1.071428571 1.214285714x + x2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 1.214285714x + x2 = 1.071428571 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 = 1.071428571 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714x + x2 = 1.071428571 + 0.3686224488 Combine like terms: 1.071428571 + 0.3686224488 = 1.4400510198 0.3686224488 + 1.214285714x + x2 = 1.4400510198 Factor a perfect square on the left side: (x + 0.607142857)(x + 0.607142857) = 1.4400510198 Calculate the square root of the right side: 1.200021258 Break this problem into two subproblems by setting (x + 0.607142857) equal to 1.200021258 and -1.200021258.Subproblem 1
x + 0.607142857 = 1.200021258 Simplifying x + 0.607142857 = 1.200021258 Reorder the terms: 0.607142857 + x = 1.200021258 Solving 0.607142857 + x = 1.200021258 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 = 1.200021258 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = 1.200021258 + -0.607142857 x = 1.200021258 + -0.607142857 Combine like terms: 1.200021258 + -0.607142857 = 0.592878401 x = 0.592878401 Simplifying x = 0.592878401Subproblem 2
x + 0.607142857 = -1.200021258 Simplifying x + 0.607142857 = -1.200021258 Reorder the terms: 0.607142857 + x = -1.200021258 Solving 0.607142857 + x = -1.200021258 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 = -1.200021258 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = -1.200021258 + -0.607142857 x = -1.200021258 + -0.607142857 Combine like terms: -1.200021258 + -0.607142857 = -1.807164115 x = -1.807164115 Simplifying x = -1.807164115Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.592878401, -1.807164115}
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