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Simplifying 18x2 + 5x + -14 = 0 Reorder the terms: -14 + 5x + 18x2 = 0 Solving -14 + 5x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.7777777778 + 0.2777777778x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 0.2777777778x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 0.2777777778x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 0.2777777778x + x2 = 0 + 0.7777777778 0.2777777778x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 0.2777777778x + x2 = 0.7777777778 The x term is 0.2777777778x. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778x + 0.01929012346 + x2 = 0.7777777778 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778x + x2 = 0.7777777778 + 0.01929012346 Combine like terms: 0.7777777778 + 0.01929012346 = 0.79706790126 0.01929012346 + 0.2777777778x + x2 = 0.79706790126 Factor a perfect square on the left side: (x + 0.1388888889)(x + 0.1388888889) = 0.79706790126 Calculate the square root of the right side: 0.892786593 Break this problem into two subproblems by setting (x + 0.1388888889) equal to 0.892786593 and -0.892786593.Subproblem 1
x + 0.1388888889 = 0.892786593 Simplifying x + 0.1388888889 = 0.892786593 Reorder the terms: 0.1388888889 + x = 0.892786593 Solving 0.1388888889 + x = 0.892786593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = 0.892786593 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = 0.892786593 + -0.1388888889 x = 0.892786593 + -0.1388888889 Combine like terms: 0.892786593 + -0.1388888889 = 0.7538977041 x = 0.7538977041 Simplifying x = 0.7538977041Subproblem 2
x + 0.1388888889 = -0.892786593 Simplifying x + 0.1388888889 = -0.892786593 Reorder the terms: 0.1388888889 + x = -0.892786593 Solving 0.1388888889 + x = -0.892786593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = -0.892786593 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = -0.892786593 + -0.1388888889 x = -0.892786593 + -0.1388888889 Combine like terms: -0.892786593 + -0.1388888889 = -1.0316754819 x = -1.0316754819 Simplifying x = -1.0316754819Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7538977041, -1.0316754819}
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