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Simplifying 9x2 + 88x + 4 = 0 Reorder the terms: 4 + 88x + 9x2 = 0 Solving 4 + 88x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + 9.777777778x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + 9.777777778x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + 9.777777778x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + 9.777777778x + x2 = 0 + -0.4444444444 9.777777778x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 9.777777778x + x2 = -0.4444444444 The x term is 9.777777778x. Take half its coefficient (4.888888889). Square it (23.90123457) and add it to both sides. Add '23.90123457' to each side of the equation. 9.777777778x + 23.90123457 + x2 = -0.4444444444 + 23.90123457 Reorder the terms: 23.90123457 + 9.777777778x + x2 = -0.4444444444 + 23.90123457 Combine like terms: -0.4444444444 + 23.90123457 = 23.4567901256 23.90123457 + 9.777777778x + x2 = 23.4567901256 Factor a perfect square on the left side: (x + 4.888888889)(x + 4.888888889) = 23.4567901256 Calculate the square root of the right side: 4.843221049 Break this problem into two subproblems by setting (x + 4.888888889) equal to 4.843221049 and -4.843221049.Subproblem 1
x + 4.888888889 = 4.843221049 Simplifying x + 4.888888889 = 4.843221049 Reorder the terms: 4.888888889 + x = 4.843221049 Solving 4.888888889 + x = 4.843221049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.888888889' to each side of the equation. 4.888888889 + -4.888888889 + x = 4.843221049 + -4.888888889 Combine like terms: 4.888888889 + -4.888888889 = 0.000000000 0.000000000 + x = 4.843221049 + -4.888888889 x = 4.843221049 + -4.888888889 Combine like terms: 4.843221049 + -4.888888889 = -0.04566784 x = -0.04566784 Simplifying x = -0.04566784Subproblem 2
x + 4.888888889 = -4.843221049 Simplifying x + 4.888888889 = -4.843221049 Reorder the terms: 4.888888889 + x = -4.843221049 Solving 4.888888889 + x = -4.843221049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.888888889' to each side of the equation. 4.888888889 + -4.888888889 + x = -4.843221049 + -4.888888889 Combine like terms: 4.888888889 + -4.888888889 = 0.000000000 0.000000000 + x = -4.843221049 + -4.888888889 x = -4.843221049 + -4.888888889 Combine like terms: -4.843221049 + -4.888888889 = -9.732109938 x = -9.732109938 Simplifying x = -9.732109938Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.04566784, -9.732109938}
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