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Simplifying x(9x + 7) = 44 Reorder the terms: x(7 + 9x) = 44 (7 * x + 9x * x) = 44 (7x + 9x2) = 44 Solving 7x + 9x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + 7x + 9x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.888888889 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '4.888888889' to each side of the equation. -4.888888889 + 0.7777777778x + 4.888888889 + x2 = 0 + 4.888888889 Reorder the terms: -4.888888889 + 4.888888889 + 0.7777777778x + x2 = 0 + 4.888888889 Combine like terms: -4.888888889 + 4.888888889 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 4.888888889 0.7777777778x + x2 = 0 + 4.888888889 Combine like terms: 0 + 4.888888889 = 4.888888889 0.7777777778x + x2 = 4.888888889 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 = 4.888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 4.888888889 + 0.1512345679 Combine like terms: 4.888888889 + 0.1512345679 = 5.0401234569 0.1512345679 + 0.7777777778x + x2 = 5.0401234569 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 5.0401234569 Calculate the square root of the right side: 2.245021928 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 2.245021928 and -2.245021928.Subproblem 1
x + 0.3888888889 = 2.245021928 Simplifying x + 0.3888888889 = 2.245021928 Reorder the terms: 0.3888888889 + x = 2.245021928 Solving 0.3888888889 + x = 2.245021928 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 = 2.245021928 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 2.245021928 + -0.3888888889 x = 2.245021928 + -0.3888888889 Combine like terms: 2.245021928 + -0.3888888889 = 1.8561330391 x = 1.8561330391 Simplifying x = 1.8561330391Subproblem 2
x + 0.3888888889 = -2.245021928 Simplifying x + 0.3888888889 = -2.245021928 Reorder the terms: 0.3888888889 + x = -2.245021928 Solving 0.3888888889 + x = -2.245021928 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 = -2.245021928 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -2.245021928 + -0.3888888889 x = -2.245021928 + -0.3888888889 Combine like terms: -2.245021928 + -0.3888888889 = -2.6339108169 x = -2.6339108169 Simplifying x = -2.6339108169Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8561330391, -2.6339108169}
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