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Simplifying x(20 + -1x) = 33.0625 (20 * x + -1x * x) = 33.0625 (20x + -1x2) = 33.0625 Solving 20x + -1x2 = 33.0625 Solving for variable 'x'. Reorder the terms: -33.0625 + 20x + -1x2 = 33.0625 + -33.0625 Combine like terms: 33.0625 + -33.0625 = 0.0000 -33.0625 + 20x + -1x2 = 0.0000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 33.0625 + -20x + x2 = 0.0000 Move the constant term to the right: Add '-33.0625' to each side of the equation. 33.0625 + -20x + -33.0625 + x2 = 0.0000 + -33.0625 Reorder the terms: 33.0625 + -33.0625 + -20x + x2 = 0.0000 + -33.0625 Combine like terms: 33.0625 + -33.0625 = 0.0000 0.0000 + -20x + x2 = 0.0000 + -33.0625 -20x + x2 = 0.0000 + -33.0625 Combine like terms: 0.0000 + -33.0625 = -33.0625 -20x + x2 = -33.0625 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -33.0625 + 100 Reorder the terms: 100 + -20x + x2 = -33.0625 + 100 Combine like terms: -33.0625 + 100 = 66.9375 100 + -20x + x2 = 66.9375 Factor a perfect square on the left side: (x + -10)(x + -10) = 66.9375 Calculate the square root of the right side: 8.181534086 Break this problem into two subproblems by setting (x + -10) equal to 8.181534086 and -8.181534086.Subproblem 1
x + -10 = 8.181534086 Simplifying x + -10 = 8.181534086 Reorder the terms: -10 + x = 8.181534086 Solving -10 + x = 8.181534086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.181534086 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.181534086 + 10 x = 8.181534086 + 10 Combine like terms: 8.181534086 + 10 = 18.181534086 x = 18.181534086 Simplifying x = 18.181534086Subproblem 2
x + -10 = -8.181534086 Simplifying x + -10 = -8.181534086 Reorder the terms: -10 + x = -8.181534086 Solving -10 + x = -8.181534086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.181534086 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.181534086 + 10 x = -8.181534086 + 10 Combine like terms: -8.181534086 + 10 = 1.818465914 x = 1.818465914 Simplifying x = 1.818465914Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.181534086, 1.818465914}
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