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Simplifying 9x2 + 2x + -0.08 = 0 Reorder the terms: -0.08 + 2x + 9x2 = 0 Solving -0.08 + 2x + 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'. -0.008888888889 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.008888888889' to each side of the equation. -0.008888888889 + 0.2222222222x + 0.008888888889 + x2 = 0 + 0.008888888889 Reorder the terms: -0.008888888889 + 0.008888888889 + 0.2222222222x + x2 = 0 + 0.008888888889 Combine like terms: -0.008888888889 + 0.008888888889 = 0.000000000000 0.000000000000 + 0.2222222222x + x2 = 0 + 0.008888888889 0.2222222222x + x2 = 0 + 0.008888888889 Combine like terms: 0 + 0.008888888889 = 0.008888888889 0.2222222222x + x2 = 0.008888888889 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 0.008888888889 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.008888888889 + 0.01234567901 Combine like terms: 0.008888888889 + 0.01234567901 = 0.021234567899 0.01234567901 + 0.2222222222x + x2 = 0.021234567899 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.021234567899 Calculate the square root of the right side: 0.145720856 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.145720856 and -0.145720856.Subproblem 1
x + 0.1111111111 = 0.145720856 Simplifying x + 0.1111111111 = 0.145720856 Reorder the terms: 0.1111111111 + x = 0.145720856 Solving 0.1111111111 + x = 0.145720856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 0.145720856 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.145720856 + -0.1111111111 x = 0.145720856 + -0.1111111111 Combine like terms: 0.145720856 + -0.1111111111 = 0.0346097449 x = 0.0346097449 Simplifying x = 0.0346097449Subproblem 2
x + 0.1111111111 = -0.145720856 Simplifying x + 0.1111111111 = -0.145720856 Reorder the terms: 0.1111111111 + x = -0.145720856 Solving 0.1111111111 + x = -0.145720856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -0.145720856 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.145720856 + -0.1111111111 x = -0.145720856 + -0.1111111111 Combine like terms: -0.145720856 + -0.1111111111 = -0.2568319671 x = -0.2568319671 Simplifying x = -0.2568319671Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0346097449, -0.2568319671}
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