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Simplifying x2 + -100x + 21 = 0 Reorder the terms: 21 + -100x + x2 = 0 Solving 21 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -100x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -100x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -100x + x2 = 0 + -21 -100x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -100x + x2 = -21 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 = -21 + 2500 Reorder the terms: 2500 + -100x + x2 = -21 + 2500 Combine like terms: -21 + 2500 = 2479 2500 + -100x + x2 = 2479 Factor a perfect square on the left side: (x + -50)(x + -50) = 2479 Calculate the square root of the right side: 49.789557138 Break this problem into two subproblems by setting (x + -50) equal to 49.789557138 and -49.789557138.Subproblem 1
x + -50 = 49.789557138 Simplifying x + -50 = 49.789557138 Reorder the terms: -50 + x = 49.789557138 Solving -50 + x = 49.789557138 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 = 49.789557138 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.789557138 + 50 x = 49.789557138 + 50 Combine like terms: 49.789557138 + 50 = 99.789557138 x = 99.789557138 Simplifying x = 99.789557138Subproblem 2
x + -50 = -49.789557138 Simplifying x + -50 = -49.789557138 Reorder the terms: -50 + x = -49.789557138 Solving -50 + x = -49.789557138 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 = -49.789557138 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.789557138 + 50 x = -49.789557138 + 50 Combine like terms: -49.789557138 + 50 = 0.210442862 x = 0.210442862 Simplifying x = 0.210442862Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.789557138, 0.210442862}
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