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Simplifying x2 + -99x + 100 = 0 Reorder the terms: 100 + -99x + x2 = 0 Solving 100 + -99x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -99x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -99x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -99x + x2 = 0 + -100 -99x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -99x + x2 = -100 The x term is -99x. Take half its coefficient (-49.5). Square it (2450.25) and add it to both sides. Add '2450.25' to each side of the equation. -99x + 2450.25 + x2 = -100 + 2450.25 Reorder the terms: 2450.25 + -99x + x2 = -100 + 2450.25 Combine like terms: -100 + 2450.25 = 2350.25 2450.25 + -99x + x2 = 2350.25 Factor a perfect square on the left side: (x + -49.5)(x + -49.5) = 2350.25 Calculate the square root of the right side: 48.479377059 Break this problem into two subproblems by setting (x + -49.5) equal to 48.479377059 and -48.479377059.Subproblem 1
x + -49.5 = 48.479377059 Simplifying x + -49.5 = 48.479377059 Reorder the terms: -49.5 + x = 48.479377059 Solving -49.5 + x = 48.479377059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.5' to each side of the equation. -49.5 + 49.5 + x = 48.479377059 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + x = 48.479377059 + 49.5 x = 48.479377059 + 49.5 Combine like terms: 48.479377059 + 49.5 = 97.979377059 x = 97.979377059 Simplifying x = 97.979377059Subproblem 2
x + -49.5 = -48.479377059 Simplifying x + -49.5 = -48.479377059 Reorder the terms: -49.5 + x = -48.479377059 Solving -49.5 + x = -48.479377059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.5' to each side of the equation. -49.5 + 49.5 + x = -48.479377059 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + x = -48.479377059 + 49.5 x = -48.479377059 + 49.5 Combine like terms: -48.479377059 + 49.5 = 1.020622941 x = 1.020622941 Simplifying x = 1.020622941Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.979377059, 1.020622941}
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