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Simplifying 9x2 = 4 + -7x Solving 9x2 = 4 + -7x Solving for variable 'x'. Reorder the terms: -4 + 7x + 9x2 = 4 + -7x + -4 + 7x Reorder the terms: -4 + 7x + 9x2 = 4 + -4 + -7x + 7x Combine like terms: 4 + -4 = 0 -4 + 7x + 9x2 = 0 + -7x + 7x -4 + 7x + 9x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -4 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.7777777778x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.7777777778x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + 0.4444444444 0.7777777778x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.7777777778x + x2 = 0.4444444444 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 = 0.4444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 0.4444444444 + 0.1512345679 Combine like terms: 0.4444444444 + 0.1512345679 = 0.5956790123 0.1512345679 + 0.7777777778x + x2 = 0.5956790123 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 0.5956790123 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 0.771802444 and -0.771802444.Subproblem 1
x + 0.3888888889 = 0.771802444 Simplifying x + 0.3888888889 = 0.771802444 Reorder the terms: 0.3888888889 + x = 0.771802444 Solving 0.3888888889 + x = 0.771802444 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 = 0.771802444 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 0.771802444 + -0.3888888889 x = 0.771802444 + -0.3888888889 Combine like terms: 0.771802444 + -0.3888888889 = 0.3829135551 x = 0.3829135551 Simplifying x = 0.3829135551Subproblem 2
x + 0.3888888889 = -0.771802444 Simplifying x + 0.3888888889 = -0.771802444 Reorder the terms: 0.3888888889 + x = -0.771802444 Solving 0.3888888889 + x = -0.771802444 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 = -0.771802444 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -0.771802444 + -0.3888888889 x = -0.771802444 + -0.3888888889 Combine like terms: -0.771802444 + -0.3888888889 = -1.1606913329 x = -1.1606913329 Simplifying x = -1.1606913329Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3829135551, -1.1606913329}
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