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Simplifying x2 + -100x + 60 = 0 Reorder the terms: 60 + -100x + x2 = 0 Solving 60 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -100x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -100x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -100x + x2 = 0 + -60 -100x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -100x + x2 = -60 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 = -60 + 2500 Reorder the terms: 2500 + -100x + x2 = -60 + 2500 Combine like terms: -60 + 2500 = 2440 2500 + -100x + x2 = 2440 Factor a perfect square on the left side: (x + -50)(x + -50) = 2440 Calculate the square root of the right side: 49.396356141 Break this problem into two subproblems by setting (x + -50) equal to 49.396356141 and -49.396356141.Subproblem 1
x + -50 = 49.396356141 Simplifying x + -50 = 49.396356141 Reorder the terms: -50 + x = 49.396356141 Solving -50 + x = 49.396356141 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 = 49.396356141 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.396356141 + 50 x = 49.396356141 + 50 Combine like terms: 49.396356141 + 50 = 99.396356141 x = 99.396356141 Simplifying x = 99.396356141Subproblem 2
x + -50 = -49.396356141 Simplifying x + -50 = -49.396356141 Reorder the terms: -50 + x = -49.396356141 Solving -50 + x = -49.396356141 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 = -49.396356141 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.396356141 + 50 x = -49.396356141 + 50 Combine like terms: -49.396356141 + 50 = 0.603643859 x = 0.603643859 Simplifying x = 0.603643859Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.396356141, 0.603643859}
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