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Simplifying 33x = 3x2 + -7x + -18 Reorder the terms: 33x = -18 + -7x + 3x2 Solving 33x = -18 + -7x + 3x2 Solving for variable 'x'. Reorder the terms: 18 + 33x + 7x + -3x2 = -18 + -7x + 3x2 + 18 + 7x + -3x2 Combine like terms: 33x + 7x = 40x 18 + 40x + -3x2 = -18 + -7x + 3x2 + 18 + 7x + -3x2 Reorder the terms: 18 + 40x + -3x2 = -18 + 18 + -7x + 7x + 3x2 + -3x2 Combine like terms: -18 + 18 = 0 18 + 40x + -3x2 = 0 + -7x + 7x + 3x2 + -3x2 18 + 40x + -3x2 = -7x + 7x + 3x2 + -3x2 Combine like terms: -7x + 7x = 0 18 + 40x + -3x2 = 0 + 3x2 + -3x2 18 + 40x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 18 + 40x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -13.33333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -13.33333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -13.33333333x + x2 = 0 + 6 -13.33333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -13.33333333x + x2 = 6 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 6 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 6 + 44.44444442 Combine like terms: 6 + 44.44444442 = 50.44444442 44.44444442 + -13.33333333x + x2 = 50.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 50.44444442 Calculate the square root of the right side: 7.102425249 Break this problem into two subproblems by setting (x + -6.666666665) equal to 7.102425249 and -7.102425249.Subproblem 1
x + -6.666666665 = 7.102425249 Simplifying x + -6.666666665 = 7.102425249 Reorder the terms: -6.666666665 + x = 7.102425249 Solving -6.666666665 + x = 7.102425249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 7.102425249 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 7.102425249 + 6.666666665 x = 7.102425249 + 6.666666665 Combine like terms: 7.102425249 + 6.666666665 = 13.769091914 x = 13.769091914 Simplifying x = 13.769091914Subproblem 2
x + -6.666666665 = -7.102425249 Simplifying x + -6.666666665 = -7.102425249 Reorder the terms: -6.666666665 + x = -7.102425249 Solving -6.666666665 + x = -7.102425249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -7.102425249 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -7.102425249 + 6.666666665 x = -7.102425249 + 6.666666665 Combine like terms: -7.102425249 + 6.666666665 = -0.435758584 x = -0.435758584 Simplifying x = -0.435758584Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.769091914, -0.435758584}
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