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Simplifying 205 = 20x + -0.075x2 Solving 205 = 20x + -0.075x2 Solving for variable 'x'. Reorder the terms: 205 + -20x + 0.075x2 = 20x + -20x + -0.075x2 + 0.075x2 Combine like terms: 20x + -20x = 0 205 + -20x + 0.075x2 = 0 + -0.075x2 + 0.075x2 205 + -20x + 0.075x2 = -0.075x2 + 0.075x2 Combine like terms: -0.075x2 + 0.075x2 = 0.000 205 + -20x + 0.075x2 = 0.000 Begin completing the square. Divide all terms by 0.075 the coefficient of the squared term: Divide each side by '0.075'. 2733.333333 + -266.6666667x + x2 = 0 Move the constant term to the right: Add '-2733.333333' to each side of the equation. 2733.333333 + -266.6666667x + -2733.333333 + x2 = 0 + -2733.333333 Reorder the terms: 2733.333333 + -2733.333333 + -266.6666667x + x2 = 0 + -2733.333333 Combine like terms: 2733.333333 + -2733.333333 = 0.000000 0.000000 + -266.6666667x + x2 = 0 + -2733.333333 -266.6666667x + x2 = 0 + -2733.333333 Combine like terms: 0 + -2733.333333 = -2733.333333 -266.6666667x + x2 = -2733.333333 The x term is -266.6666667x. Take half its coefficient (-133.3333334). Square it (17777.77780) and add it to both sides. Add '17777.77780' to each side of the equation. -266.6666667x + 17777.77780 + x2 = -2733.333333 + 17777.77780 Reorder the terms: 17777.77780 + -266.6666667x + x2 = -2733.333333 + 17777.77780 Combine like terms: -2733.333333 + 17777.77780 = 15044.444467 17777.77780 + -266.6666667x + x2 = 15044.444467 Factor a perfect square on the left side: (x + -133.3333334)(x + -133.3333334) = 15044.444467 Calculate the square root of the right side: 122.655796712 Break this problem into two subproblems by setting (x + -133.3333334) equal to 122.655796712 and -122.655796712.Subproblem 1
x + -133.3333334 = 122.655796712 Simplifying x + -133.3333334 = 122.655796712 Reorder the terms: -133.3333334 + x = 122.655796712 Solving -133.3333334 + x = 122.655796712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = 122.655796712 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = 122.655796712 + 133.3333334 x = 122.655796712 + 133.3333334 Combine like terms: 122.655796712 + 133.3333334 = 255.989130112 x = 255.989130112 Simplifying x = 255.989130112Subproblem 2
x + -133.3333334 = -122.655796712 Simplifying x + -133.3333334 = -122.655796712 Reorder the terms: -133.3333334 + x = -122.655796712 Solving -133.3333334 + x = -122.655796712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = -122.655796712 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = -122.655796712 + 133.3333334 x = -122.655796712 + 133.3333334 Combine like terms: -122.655796712 + 133.3333334 = 10.677536688 x = 10.677536688 Simplifying x = 10.677536688Solution
The solution to the problem is based on the solutions from the subproblems. x = {255.989130112, 10.677536688}
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