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Simplifying (-18x2) + -33x + -4 = x Reorder the terms: -4 + -33x + (-18x2) = x Solving -4 + -33x + (-18x2) = x Solving for variable 'x'. Reorder the terms: -4 + -33x + -1x + (-18x2) = x + -1x Combine like terms: -33x + -1x = -34x -4 + -34x + (-18x2) = x + -1x Combine like terms: x + -1x = 0 -4 + -34x + (-18x2) = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 17x + (9x2)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 17x + (9x2))' equal to zero and attempt to solve: Simplifying 2 + 17x + (9x2) = 0 Solving 2 + 17x + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 1.888888889x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 1.888888889x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 1.888888889x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 1.888888889x + x2 = 0 + -0.2222222222 1.888888889x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 1.888888889x + x2 = -0.2222222222 The x term is 1.888888889x. Take half its coefficient (0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. 1.888888889x + 0.8919753087 + x2 = -0.2222222222 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889x + x2 = -0.2222222222 + 0.8919753087 Combine like terms: -0.2222222222 + 0.8919753087 = 0.6697530865 0.8919753087 + 1.888888889x + x2 = 0.6697530865 Factor a perfect square on the left side: ((x) + 0.9444444445)((x) + 0.9444444445) = 0.6697530865 Calculate the square root of the right side: 0.818384437 Break this problem into two subproblems by setting ((x) + 0.9444444445) equal to 0.818384437 and -0.818384437.Subproblem 1
(x) + 0.9444444445 = 0.818384437 Simplifying (x) + 0.9444444445 = 0.818384437 x + 0.9444444445 = 0.818384437 Reorder the terms: 0.9444444445 + x = 0.818384437 Solving 0.9444444445 + x = 0.818384437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = 0.818384437 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 0.818384437 + -0.9444444445 x = 0.818384437 + -0.9444444445 Combine like terms: 0.818384437 + -0.9444444445 = -0.1260600075 x = -0.1260600075 Simplifying x = -0.1260600075Subproblem 2
(x) + 0.9444444445 = -0.818384437 Simplifying (x) + 0.9444444445 = -0.818384437 x + 0.9444444445 = -0.818384437 Reorder the terms: 0.9444444445 + x = -0.818384437 Solving 0.9444444445 + x = -0.818384437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = -0.818384437 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -0.818384437 + -0.9444444445 x = -0.818384437 + -0.9444444445 Combine like terms: -0.818384437 + -0.9444444445 = -1.7628288815 x = -1.7628288815 Simplifying x = -1.7628288815Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1260600075, -1.7628288815}Solution
x = {-0.1260600075, -1.7628288815}
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