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Simplifying -0.33x2 + 38.28x + 5861.32 = 6628 Reorder the terms: 5861.32 + 38.28x + -0.33x2 = 6628 Solving 5861.32 + 38.28x + -0.33x2 = 6628 Solving for variable 'x'. Reorder the terms: 5861.32 + -6628 + 38.28x + -0.33x2 = 6628 + -6628 Combine like terms: 5861.32 + -6628 = -766.68 -766.68 + 38.28x + -0.33x2 = 6628 + -6628 Combine like terms: 6628 + -6628 = 0 -766.68 + 38.28x + -0.33x2 = 0 Begin completing the square. Divide all terms by -0.33 the coefficient of the squared term: Divide each side by '-0.33'. 2323.272727 + -116x + x2 = 0 Move the constant term to the right: Add '-2323.272727' to each side of the equation. 2323.272727 + -116x + -2323.272727 + x2 = 0 + -2323.272727 Reorder the terms: 2323.272727 + -2323.272727 + -116x + x2 = 0 + -2323.272727 Combine like terms: 2323.272727 + -2323.272727 = 0.000000 0.000000 + -116x + x2 = 0 + -2323.272727 -116x + x2 = 0 + -2323.272727 Combine like terms: 0 + -2323.272727 = -2323.272727 -116x + x2 = -2323.272727 The x term is -116x. Take half its coefficient (-58). Square it (3364) and add it to both sides. Add '3364' to each side of the equation. -116x + 3364 + x2 = -2323.272727 + 3364 Reorder the terms: 3364 + -116x + x2 = -2323.272727 + 3364 Combine like terms: -2323.272727 + 3364 = 1040.727273 3364 + -116x + x2 = 1040.727273 Factor a perfect square on the left side: (x + -58)(x + -58) = 1040.727273 Calculate the square root of the right side: 32.260304912 Break this problem into two subproblems by setting (x + -58) equal to 32.260304912 and -32.260304912.Subproblem 1
x + -58 = 32.260304912 Simplifying x + -58 = 32.260304912 Reorder the terms: -58 + x = 32.260304912 Solving -58 + x = 32.260304912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = 32.260304912 + 58 Combine like terms: -58 + 58 = 0 0 + x = 32.260304912 + 58 x = 32.260304912 + 58 Combine like terms: 32.260304912 + 58 = 90.260304912 x = 90.260304912 Simplifying x = 90.260304912Subproblem 2
x + -58 = -32.260304912 Simplifying x + -58 = -32.260304912 Reorder the terms: -58 + x = -32.260304912 Solving -58 + x = -32.260304912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = -32.260304912 + 58 Combine like terms: -58 + 58 = 0 0 + x = -32.260304912 + 58 x = -32.260304912 + 58 Combine like terms: -32.260304912 + 58 = 25.739695088 x = 25.739695088 Simplifying x = 25.739695088Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.260304912, 25.739695088}
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