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Simplifying 9x2 + 16x + -2 = 0 Reorder the terms: -2 + 16x + 9x2 = 0 Solving -2 + 16x + 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'. -0.2222222222 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 1.777777778x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 1.777777778x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 1.777777778x + x2 = 0 + 0.2222222222 1.777777778x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 1.777777778x + x2 = 0.2222222222 The x term is 1.777777778x. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778x + 0.7901234570 + x2 = 0.2222222222 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = 0.2222222222 + 0.7901234570 Combine like terms: 0.2222222222 + 0.7901234570 = 1.0123456792 0.7901234570 + 1.777777778x + x2 = 1.0123456792 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = 1.0123456792 Calculate the square root of the right side: 1.006153904 Break this problem into two subproblems by setting (x + 0.888888889) equal to 1.006153904 and -1.006153904.Subproblem 1
x + 0.888888889 = 1.006153904 Simplifying x + 0.888888889 = 1.006153904 Reorder the terms: 0.888888889 + x = 1.006153904 Solving 0.888888889 + x = 1.006153904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = 1.006153904 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = 1.006153904 + -0.888888889 x = 1.006153904 + -0.888888889 Combine like terms: 1.006153904 + -0.888888889 = 0.117265015 x = 0.117265015 Simplifying x = 0.117265015Subproblem 2
x + 0.888888889 = -1.006153904 Simplifying x + 0.888888889 = -1.006153904 Reorder the terms: 0.888888889 + x = -1.006153904 Solving 0.888888889 + x = -1.006153904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = -1.006153904 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = -1.006153904 + -0.888888889 x = -1.006153904 + -0.888888889 Combine like terms: -1.006153904 + -0.888888889 = -1.895042793 x = -1.895042793 Simplifying x = -1.895042793Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.117265015, -1.895042793}
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