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Simplifying -0.03289(x + -62.5)(x + -62.5) + 225 = -0.8x + 140 Reorder the terms: -0.03289(-62.5 + x)(x + -62.5) + 225 = -0.8x + 140 Reorder the terms: -0.03289(-62.5 + x)(-62.5 + x) + 225 = -0.8x + 140 Multiply (-62.5 + x) * (-62.5 + x) -0.03289(-62.5(-62.5 + x) + x(-62.5 + x)) + 225 = -0.8x + 140 -0.03289((-62.5 * -62.5 + x * -62.5) + x(-62.5 + x)) + 225 = -0.8x + 140 -0.03289((3906.25 + -62.5x) + x(-62.5 + x)) + 225 = -0.8x + 140 -0.03289(3906.25 + -62.5x + (-62.5 * x + x * x)) + 225 = -0.8x + 140 -0.03289(3906.25 + -62.5x + (-62.5x + x2)) + 225 = -0.8x + 140 Combine like terms: -62.5x + -62.5x = -125x -0.03289(3906.25 + -125x + x2) + 225 = -0.8x + 140 (3906.25 * -0.03289 + -125x * -0.03289 + x2 * -0.03289) + 225 = -0.8x + 140 (-128.4765625 + 4.11125x + -0.03289x2) + 225 = -0.8x + 140 Reorder the terms: -128.4765625 + 225 + 4.11125x + -0.03289x2 = -0.8x + 140 Combine like terms: -128.4765625 + 225 = 96.5234375 96.5234375 + 4.11125x + -0.03289x2 = -0.8x + 140 Reorder the terms: 96.5234375 + 4.11125x + -0.03289x2 = 140 + -0.8x Solving 96.5234375 + 4.11125x + -0.03289x2 = 140 + -0.8x Solving for variable 'x'. Reorder the terms: 96.5234375 + -140 + 4.11125x + 0.8x + -0.03289x2 = 140 + -0.8x + -140 + 0.8x Combine like terms: 96.5234375 + -140 = -43.4765625 -43.4765625 + 4.11125x + 0.8x + -0.03289x2 = 140 + -0.8x + -140 + 0.8x Combine like terms: 4.11125x + 0.8x = 4.91125x -43.4765625 + 4.91125x + -0.03289x2 = 140 + -0.8x + -140 + 0.8x Reorder the terms: -43.4765625 + 4.91125x + -0.03289x2 = 140 + -140 + -0.8x + 0.8x Combine like terms: 140 + -140 = 0 -43.4765625 + 4.91125x + -0.03289x2 = 0 + -0.8x + 0.8x -43.4765625 + 4.91125x + -0.03289x2 = -0.8x + 0.8x Combine like terms: -0.8x + 0.8x = 0.0 -43.4765625 + 4.91125x + -0.03289x2 = 0.0 Begin completing the square. Divide all terms by -0.03289 the coefficient of the squared term: Divide each side by '-0.03289'. 1321.87785 + -149.3235026x + x2 = 0 Move the constant term to the right: Add '-1321.87785' to each side of the equation. 1321.87785 + -149.3235026x + -1321.87785 + x2 = 0 + -1321.87785 Reorder the terms: 1321.87785 + -1321.87785 + -149.3235026x + x2 = 0 + -1321.87785 Combine like terms: 1321.87785 + -1321.87785 = 0.00000 0.00000 + -149.3235026x + x2 = 0 + -1321.87785 -149.3235026x + x2 = 0 + -1321.87785 Combine like terms: 0 + -1321.87785 = -1321.87785 -149.3235026x + x2 = -1321.87785 The x term is -149.3235026x. Take half its coefficient (-74.6617513). Square it (5574.377107) and add it to both sides. Add '5574.377107' to each side of the equation. -149.3235026x + 5574.377107 + x2 = -1321.87785 + 5574.377107 Reorder the terms: 5574.377107 + -149.3235026x + x2 = -1321.87785 + 5574.377107 Combine like terms: -1321.87785 + 5574.377107 = 4252.499257 5574.377107 + -149.3235026x + x2 = 4252.499257 Factor a perfect square on the left side: (x + -74.6617513)(x + -74.6617513) = 4252.499257 Calculate the square root of the right side: 65.211189661 Break this problem into two subproblems by setting (x + -74.6617513) equal to 65.211189661 and -65.211189661.Subproblem 1
x + -74.6617513 = 65.211189661 Simplifying x + -74.6617513 = 65.211189661 Reorder the terms: -74.6617513 + x = 65.211189661 Solving -74.6617513 + x = 65.211189661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '74.6617513' to each side of the equation. -74.6617513 + 74.6617513 + x = 65.211189661 + 74.6617513 Combine like terms: -74.6617513 + 74.6617513 = 0.0000000 0.0000000 + x = 65.211189661 + 74.6617513 x = 65.211189661 + 74.6617513 Combine like terms: 65.211189661 + 74.6617513 = 139.872940961 x = 139.872940961 Simplifying x = 139.872940961Subproblem 2
x + -74.6617513 = -65.211189661 Simplifying x + -74.6617513 = -65.211189661 Reorder the terms: -74.6617513 + x = -65.211189661 Solving -74.6617513 + x = -65.211189661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '74.6617513' to each side of the equation. -74.6617513 + 74.6617513 + x = -65.211189661 + 74.6617513 Combine like terms: -74.6617513 + 74.6617513 = 0.0000000 0.0000000 + x = -65.211189661 + 74.6617513 x = -65.211189661 + 74.6617513 Combine like terms: -65.211189661 + 74.6617513 = 9.450561639 x = 9.450561639 Simplifying x = 9.450561639Solution
The solution to the problem is based on the solutions from the subproblems. x = {139.872940961, 9.450561639}
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