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Simplifying 14x2 + -17x + -5 = 0 Reorder the terms: -5 + -17x + 14x2 = 0 Solving -5 + -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'. -0.3571428571 + -1.214285714x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -1.214285714x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -1.214285714x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -1.214285714x + x2 = 0 + 0.3571428571 -1.214285714x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -1.214285714x + x2 = 0.3571428571 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 = 0.3571428571 + 0.3686224488 Reorder the terms: 0.3686224488 + -1.214285714x + x2 = 0.3571428571 + 0.3686224488 Combine like terms: 0.3571428571 + 0.3686224488 = 0.7257653059 0.3686224488 + -1.214285714x + x2 = 0.7257653059 Factor a perfect square on the left side: (x + -0.607142857)(x + -0.607142857) = 0.7257653059 Calculate the square root of the right side: 0.851918603 Break this problem into two subproblems by setting (x + -0.607142857) equal to 0.851918603 and -0.851918603.Subproblem 1
x + -0.607142857 = 0.851918603 Simplifying x + -0.607142857 = 0.851918603 Reorder the terms: -0.607142857 + x = 0.851918603 Solving -0.607142857 + x = 0.851918603 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 = 0.851918603 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + x = 0.851918603 + 0.607142857 x = 0.851918603 + 0.607142857 Combine like terms: 0.851918603 + 0.607142857 = 1.45906146 x = 1.45906146 Simplifying x = 1.45906146Subproblem 2
x + -0.607142857 = -0.851918603 Simplifying x + -0.607142857 = -0.851918603 Reorder the terms: -0.607142857 + x = -0.851918603 Solving -0.607142857 + x = -0.851918603 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 = -0.851918603 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + x = -0.851918603 + 0.607142857 x = -0.851918603 + 0.607142857 Combine like terms: -0.851918603 + 0.607142857 = -0.244775746 x = -0.244775746 Simplifying x = -0.244775746Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.45906146, -0.244775746}
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