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Simplifying x2 + -100x + 4 = 0 Reorder the terms: 4 + -100x + x2 = 0 Solving 4 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -100x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -100x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -100x + x2 = 0 + -4 -100x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -100x + x2 = -4 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 = -4 + 2500 Reorder the terms: 2500 + -100x + x2 = -4 + 2500 Combine like terms: -4 + 2500 = 2496 2500 + -100x + x2 = 2496 Factor a perfect square on the left side: (x + -50)(x + -50) = 2496 Calculate the square root of the right side: 49.959983987 Break this problem into two subproblems by setting (x + -50) equal to 49.959983987 and -49.959983987.Subproblem 1
x + -50 = 49.959983987 Simplifying x + -50 = 49.959983987 Reorder the terms: -50 + x = 49.959983987 Solving -50 + x = 49.959983987 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 = 49.959983987 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.959983987 + 50 x = 49.959983987 + 50 Combine like terms: 49.959983987 + 50 = 99.959983987 x = 99.959983987 Simplifying x = 99.959983987Subproblem 2
x + -50 = -49.959983987 Simplifying x + -50 = -49.959983987 Reorder the terms: -50 + x = -49.959983987 Solving -50 + x = -49.959983987 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 = -49.959983987 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.959983987 + 50 x = -49.959983987 + 50 Combine like terms: -49.959983987 + 50 = 0.040016013 x = 0.040016013 Simplifying x = 0.040016013Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.959983987, 0.040016013}
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