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Simplifying x(15.5 + -1x) = 40 (15.5 * x + -1x * x) = 40 (15.5x + -1x2) = 40 Solving 15.5x + -1x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 15.5x + -1x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 15.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -15.5x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -15.5x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -15.5x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -15.5x + x2 = 0 + -40 -15.5x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -15.5x + x2 = -40 The x term is -15.5x. Take half its coefficient (-7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. -15.5x + 60.0625 + x2 = -40 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = -40 + 60.0625 Combine like terms: -40 + 60.0625 = 20.0625 60.0625 + -15.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + -7.75) equal to 4.479118217 and -4.479118217.Subproblem 1
x + -7.75 = 4.479118217 Simplifying x + -7.75 = 4.479118217 Reorder the terms: -7.75 + x = 4.479118217 Solving -7.75 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = 4.479118217 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 4.479118217 + 7.75 x = 4.479118217 + 7.75 Combine like terms: 4.479118217 + 7.75 = 12.229118217 x = 12.229118217 Simplifying x = 12.229118217Subproblem 2
x + -7.75 = -4.479118217 Simplifying x + -7.75 = -4.479118217 Reorder the terms: -7.75 + x = -4.479118217 Solving -7.75 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = -4.479118217 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -4.479118217 + 7.75 x = -4.479118217 + 7.75 Combine like terms: -4.479118217 + 7.75 = 3.270881783 x = 3.270881783 Simplifying x = 3.270881783Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.229118217, 3.270881783}
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