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Simplifying x(100 + -1x) = 0.0694501558059416435927662179821 (100 * x + -1x * x) = 0.0694501558059416435927662179821 (100x + -1x2) = 0.0694501558059416435927662179821 Solving 100x + -1x2 = 0.0694501558059416435927662179821 Solving for variable 'x'. Reorder the terms: -0.0694501558059416435927662179821 + 100x + -1x2 = 0.0694501558059416435927662179821 + -0.0694501558059416435927662179821 Combine like terms: 0.0694501558059416435927662179821 + -0.0694501558059416435927662179821 = 0.0000000000000000000000000000000 -0.0694501558059416435927662179821 + 100x + -1x2 = 0.0000000000000000000000000000000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.06945015581 + -100x + x2 = 0.0000000000000000000000000000000 Move the constant term to the right: Add '-0.06945015581' to each side of the equation. 0.06945015581 + -100x + -0.06945015581 + x2 = 0.0000000000000000000000000000000 + -0.06945015581 Reorder the terms: 0.06945015581 + -0.06945015581 + -100x + x2 = 0.0000000000000000000000000000000 + -0.06945015581 Combine like terms: 0.06945015581 + -0.06945015581 = 0.00000000000 0.00000000000 + -100x + x2 = 0.0000000000000000000000000000000 + -0.06945015581 -100x + x2 = 0.0000000000000000000000000000000 + -0.06945015581 Combine like terms: 0.0000000000000000000000000000000 + -0.06945015581 = -0.06945015581 -100x + x2 = -0.06945015581 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -0.06945015581 + 2500 Reorder the terms: 2500 + -100x + x2 = -0.06945015581 + 2500 Combine like terms: -0.06945015581 + 2500 = 2499.93054984419 2500 + -100x + x2 = 2499.93054984419 Factor a perfect square on the left side: (x + -50)(x + -50) = 2499.93054984419 Calculate the square root of the right side: 49.999305494 Break this problem into two subproblems by setting (x + -50) equal to 49.999305494 and -49.999305494.Subproblem 1
x + -50 = 49.999305494 Simplifying x + -50 = 49.999305494 Reorder the terms: -50 + x = 49.999305494 Solving -50 + x = 49.999305494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 49.999305494 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.999305494 + 50 x = 49.999305494 + 50 Combine like terms: 49.999305494 + 50 = 99.999305494 x = 99.999305494 Simplifying x = 99.999305494Subproblem 2
x + -50 = -49.999305494 Simplifying x + -50 = -49.999305494 Reorder the terms: -50 + x = -49.999305494 Solving -50 + x = -49.999305494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -49.999305494 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.999305494 + 50 x = -49.999305494 + 50 Combine like terms: -49.999305494 + 50 = 0.000694506 x = 0.000694506 Simplifying x = 0.000694506Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.999305494, 0.000694506}
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