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Simplifying (0.184x2) + -1(0.08x) = 0.0225 Remove parenthesis around (0.08x) (0.184x2) + -1 * 0.08x = 0.0225 Multiply -1 * 0.08 (0.184x2) + -0.08x = 0.0225 Reorder the terms: -0.08x + (0.184x2) = 0.0225 Solving -0.08x + (0.184x2) = 0.0225 Solving for variable 'x'. Reorder the terms: -0.0225 + -0.08x + (0.184x2) = 0.0225 + -0.0225 Combine like terms: 0.0225 + -0.0225 = 0.0000 -0.0225 + -0.08x + (0.184x2) = 0.0000 Begin completing the square. Divide all terms by 0.184 the coefficient of the squared term: Divide each side by '0.184'. -0.1222826087 + -0.4347826087x + x2 = 0.0 Move the constant term to the right: Add '0.1222826087' to each side of the equation. -0.1222826087 + -0.4347826087x + 0.1222826087 + x2 = 0.0 + 0.1222826087 Reorder the terms: -0.1222826087 + 0.1222826087 + -0.4347826087x + x2 = 0.0 + 0.1222826087 Combine like terms: -0.1222826087 + 0.1222826087 = 0.0000000000 0.0000000000 + -0.4347826087x + x2 = 0.0 + 0.1222826087 -0.4347826087x + x2 = 0.0 + 0.1222826087 Combine like terms: 0.0 + 0.1222826087 = 0.1222826087 -0.4347826087x + x2 = 0.1222826087 The x term is -0.4347826087x. Take half its coefficient (-0.2173913044). Square it (0.04725897923) and add it to both sides. Add '0.04725897923' to each side of the equation. -0.4347826087x + 0.04725897923 + x2 = 0.1222826087 + 0.04725897923 Reorder the terms: 0.04725897923 + -0.4347826087x + x2 = 0.1222826087 + 0.04725897923 Combine like terms: 0.1222826087 + 0.04725897923 = 0.16954158793 0.04725897923 + -0.4347826087x + x2 = 0.16954158793 Factor a perfect square on the left side: ((x) + -0.2173913044)((x) + -0.2173913044) = 0.16954158793 Calculate the square root of the right side: 0.411754281 Break this problem into two subproblems by setting ((x) + -0.2173913044) equal to 0.411754281 and -0.411754281.Subproblem 1
(x) + -0.2173913044 = 0.411754281 Simplifying (x) + -0.2173913044 = 0.411754281 x + -0.2173913044 = 0.411754281 Reorder the terms: -0.2173913044 + x = 0.411754281 Solving -0.2173913044 + x = 0.411754281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2173913044' to each side of the equation. -0.2173913044 + 0.2173913044 + x = 0.411754281 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = 0.411754281 + 0.2173913044 x = 0.411754281 + 0.2173913044 Combine like terms: 0.411754281 + 0.2173913044 = 0.6291455854 x = 0.6291455854 Simplifying x = 0.6291455854Subproblem 2
(x) + -0.2173913044 = -0.411754281 Simplifying (x) + -0.2173913044 = -0.411754281 x + -0.2173913044 = -0.411754281 Reorder the terms: -0.2173913044 + x = -0.411754281 Solving -0.2173913044 + x = -0.411754281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2173913044' to each side of the equation. -0.2173913044 + 0.2173913044 + x = -0.411754281 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = -0.411754281 + 0.2173913044 x = -0.411754281 + 0.2173913044 Combine like terms: -0.411754281 + 0.2173913044 = -0.1943629766 x = -0.1943629766 Simplifying x = -0.1943629766Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6291455854, -0.1943629766}
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