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Simplifying 18x2 + 14x + -7 = 0 Reorder the terms: -7 + 14x + 18x2 = 0 Solving -7 + 14x + 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'. -0.3888888889 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.7777777778x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + 0.7777777778x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + 0.3888888889 0.7777777778x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 0.7777777778x + x2 = 0.3888888889 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 0.3888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 0.3888888889 + 0.1512345679 Combine like terms: 0.3888888889 + 0.1512345679 = 0.5401234568 0.1512345679 + 0.7777777778x + x2 = 0.5401234568 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 0.5401234568 Calculate the square root of the right side: 0.73493092 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 0.73493092 and -0.73493092.Subproblem 1
x + 0.3888888889 = 0.73493092 Simplifying x + 0.3888888889 = 0.73493092 Reorder the terms: 0.3888888889 + x = 0.73493092 Solving 0.3888888889 + x = 0.73493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 0.73493092 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 0.73493092 + -0.3888888889 x = 0.73493092 + -0.3888888889 Combine like terms: 0.73493092 + -0.3888888889 = 0.3460420311 x = 0.3460420311 Simplifying x = 0.3460420311Subproblem 2
x + 0.3888888889 = -0.73493092 Simplifying x + 0.3888888889 = -0.73493092 Reorder the terms: 0.3888888889 + x = -0.73493092 Solving 0.3888888889 + x = -0.73493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -0.73493092 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -0.73493092 + -0.3888888889 x = -0.73493092 + -0.3888888889 Combine like terms: -0.73493092 + -0.3888888889 = -1.1238198089 x = -1.1238198089 Simplifying x = -1.1238198089Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3460420311, -1.1238198089}
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