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Simplifying 99x2 + -10000x + 100 = 0 Reorder the terms: 100 + -10000x + 99x2 = 0 Solving 100 + -10000x + 99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. 1.01010101 + -101.010101x + x2 = 0 Move the constant term to the right: Add '-1.01010101' to each side of the equation. 1.01010101 + -101.010101x + -1.01010101 + x2 = 0 + -1.01010101 Reorder the terms: 1.01010101 + -1.01010101 + -101.010101x + x2 = 0 + -1.01010101 Combine like terms: 1.01010101 + -1.01010101 = 0.00000000 0.00000000 + -101.010101x + x2 = 0 + -1.01010101 -101.010101x + x2 = 0 + -1.01010101 Combine like terms: 0 + -1.01010101 = -1.01010101 -101.010101x + x2 = -1.01010101 The x term is -101.010101x. Take half its coefficient (-50.5050505). Square it (2550.760126) and add it to both sides. Add '2550.760126' to each side of the equation. -101.010101x + 2550.760126 + x2 = -1.01010101 + 2550.760126 Reorder the terms: 2550.760126 + -101.010101x + x2 = -1.01010101 + 2550.760126 Combine like terms: -1.01010101 + 2550.760126 = 2549.75002499 2550.760126 + -101.010101x + x2 = 2549.75002499 Factor a perfect square on the left side: (x + -50.5050505)(x + -50.5050505) = 2549.75002499 Calculate the square root of the right side: 50.49504951 Break this problem into two subproblems by setting (x + -50.5050505) equal to 50.49504951 and -50.49504951.Subproblem 1
x + -50.5050505 = 50.49504951 Simplifying x + -50.5050505 = 50.49504951 Reorder the terms: -50.5050505 + x = 50.49504951 Solving -50.5050505 + x = 50.49504951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.5050505' to each side of the equation. -50.5050505 + 50.5050505 + x = 50.49504951 + 50.5050505 Combine like terms: -50.5050505 + 50.5050505 = 0.0000000 0.0000000 + x = 50.49504951 + 50.5050505 x = 50.49504951 + 50.5050505 Combine like terms: 50.49504951 + 50.5050505 = 101.00010001 x = 101.00010001 Simplifying x = 101.00010001Subproblem 2
x + -50.5050505 = -50.49504951 Simplifying x + -50.5050505 = -50.49504951 Reorder the terms: -50.5050505 + x = -50.49504951 Solving -50.5050505 + x = -50.49504951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.5050505' to each side of the equation. -50.5050505 + 50.5050505 + x = -50.49504951 + 50.5050505 Combine like terms: -50.5050505 + 50.5050505 = 0.0000000 0.0000000 + x = -50.49504951 + 50.5050505 x = -50.49504951 + 50.5050505 Combine like terms: -50.49504951 + 50.5050505 = 0.01000099 x = 0.01000099 Simplifying x = 0.01000099Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.00010001, 0.01000099}
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