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Simplifying x(9x + 7) = 14 Reorder the terms: x(7 + 9x) = 14 (7 * x + 9x * x) = 14 (7x + 9x2) = 14 Solving 7x + 9x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 7x + 9x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 0.7777777778x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 0.7777777778x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 1.555555556 0.7777777778x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 0.7777777778x + x2 = 1.555555556 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 = 1.555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 1.555555556 + 0.1512345679 Combine like terms: 1.555555556 + 0.1512345679 = 1.7067901239 0.1512345679 + 0.7777777778x + x2 = 1.7067901239 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 1.7067901239 Calculate the square root of the right side: 1.30644178 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.30644178 and -1.30644178.Subproblem 1
x + 0.3888888889 = 1.30644178 Simplifying x + 0.3888888889 = 1.30644178 Reorder the terms: 0.3888888889 + x = 1.30644178 Solving 0.3888888889 + x = 1.30644178 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 = 1.30644178 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.30644178 + -0.3888888889 x = 1.30644178 + -0.3888888889 Combine like terms: 1.30644178 + -0.3888888889 = 0.9175528911 x = 0.9175528911 Simplifying x = 0.9175528911Subproblem 2
x + 0.3888888889 = -1.30644178 Simplifying x + 0.3888888889 = -1.30644178 Reorder the terms: 0.3888888889 + x = -1.30644178 Solving 0.3888888889 + x = -1.30644178 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 = -1.30644178 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.30644178 + -0.3888888889 x = -1.30644178 + -0.3888888889 Combine like terms: -1.30644178 + -0.3888888889 = -1.6953306689 x = -1.6953306689 Simplifying x = -1.6953306689Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9175528911, -1.6953306689}
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