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Simplifying 5x + 3x(40 + -1x) = 180 5x + (40 * 3x + -1x * 3x) = 180 5x + (120x + -3x2) = 180 Combine like terms: 5x + 120x = 125x 125x + -3x2 = 180 Solving 125x + -3x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 125x + -3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 125x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 60 + -41.66666667x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -41.66666667x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -41.66666667x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -41.66666667x + x2 = 0 + -60 -41.66666667x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -41.66666667x + x2 = -60 The x term is -41.66666667x. Take half its coefficient (-20.83333334). Square it (434.0277781) and add it to both sides. Add '434.0277781' to each side of the equation. -41.66666667x + 434.0277781 + x2 = -60 + 434.0277781 Reorder the terms: 434.0277781 + -41.66666667x + x2 = -60 + 434.0277781 Combine like terms: -60 + 434.0277781 = 374.0277781 434.0277781 + -41.66666667x + x2 = 374.0277781 Factor a perfect square on the left side: (x + -20.83333334)(x + -20.83333334) = 374.0277781 Calculate the square root of the right side: 19.339797778 Break this problem into two subproblems by setting (x + -20.83333334) equal to 19.339797778 and -19.339797778.Subproblem 1
x + -20.83333334 = 19.339797778 Simplifying x + -20.83333334 = 19.339797778 Reorder the terms: -20.83333334 + x = 19.339797778 Solving -20.83333334 + x = 19.339797778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.83333334' to each side of the equation. -20.83333334 + 20.83333334 + x = 19.339797778 + 20.83333334 Combine like terms: -20.83333334 + 20.83333334 = 0.00000000 0.00000000 + x = 19.339797778 + 20.83333334 x = 19.339797778 + 20.83333334 Combine like terms: 19.339797778 + 20.83333334 = 40.173131118 x = 40.173131118 Simplifying x = 40.173131118Subproblem 2
x + -20.83333334 = -19.339797778 Simplifying x + -20.83333334 = -19.339797778 Reorder the terms: -20.83333334 + x = -19.339797778 Solving -20.83333334 + x = -19.339797778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.83333334' to each side of the equation. -20.83333334 + 20.83333334 + x = -19.339797778 + 20.83333334 Combine like terms: -20.83333334 + 20.83333334 = 0.00000000 0.00000000 + x = -19.339797778 + 20.83333334 x = -19.339797778 + 20.83333334 Combine like terms: -19.339797778 + 20.83333334 = 1.493535562 x = 1.493535562 Simplifying x = 1.493535562Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.173131118, 1.493535562}
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