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Simplifying x2 + -100x + 1 = 0 Reorder the terms: 1 + -100x + x2 = 0 Solving 1 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -100x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -100x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -100x + x2 = 0 + -1 -100x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -100x + x2 = -1 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 = -1 + 2500 Reorder the terms: 2500 + -100x + x2 = -1 + 2500 Combine like terms: -1 + 2500 = 2499 2500 + -100x + x2 = 2499 Factor a perfect square on the left side: (x + -50)(x + -50) = 2499 Calculate the square root of the right side: 49.989999 Break this problem into two subproblems by setting (x + -50) equal to 49.989999 and -49.989999.Subproblem 1
x + -50 = 49.989999 Simplifying x + -50 = 49.989999 Reorder the terms: -50 + x = 49.989999 Solving -50 + x = 49.989999 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 = 49.989999 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.989999 + 50 x = 49.989999 + 50 Combine like terms: 49.989999 + 50 = 99.989999 x = 99.989999 Simplifying x = 99.989999Subproblem 2
x + -50 = -49.989999 Simplifying x + -50 = -49.989999 Reorder the terms: -50 + x = -49.989999 Solving -50 + x = -49.989999 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 = -49.989999 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.989999 + 50 x = -49.989999 + 50 Combine like terms: -49.989999 + 50 = 0.010001 x = 0.010001 Simplifying x = 0.010001Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.989999, 0.010001}
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