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Simplifying x2 + 101x + -16 = 0 Reorder the terms: -16 + 101x + x2 = 0 Solving -16 + 101x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 101x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 101x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 101x + x2 = 0 + 16 101x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 101x + x2 = 16 The x term is 101x. Take half its coefficient (50.5). Square it (2550.25) and add it to both sides. Add '2550.25' to each side of the equation. 101x + 2550.25 + x2 = 16 + 2550.25 Reorder the terms: 2550.25 + 101x + x2 = 16 + 2550.25 Combine like terms: 16 + 2550.25 = 2566.25 2550.25 + 101x + x2 = 2566.25 Factor a perfect square on the left side: (x + 50.5)(x + 50.5) = 2566.25 Calculate the square root of the right side: 50.658168147 Break this problem into two subproblems by setting (x + 50.5) equal to 50.658168147 and -50.658168147.Subproblem 1
x + 50.5 = 50.658168147 Simplifying x + 50.5 = 50.658168147 Reorder the terms: 50.5 + x = 50.658168147 Solving 50.5 + x = 50.658168147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.5' to each side of the equation. 50.5 + -50.5 + x = 50.658168147 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 0.0 + x = 50.658168147 + -50.5 x = 50.658168147 + -50.5 Combine like terms: 50.658168147 + -50.5 = 0.158168147 x = 0.158168147 Simplifying x = 0.158168147Subproblem 2
x + 50.5 = -50.658168147 Simplifying x + 50.5 = -50.658168147 Reorder the terms: 50.5 + x = -50.658168147 Solving 50.5 + x = -50.658168147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.5' to each side of the equation. 50.5 + -50.5 + x = -50.658168147 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 0.0 + x = -50.658168147 + -50.5 x = -50.658168147 + -50.5 Combine like terms: -50.658168147 + -50.5 = -101.158168147 x = -101.158168147 Simplifying x = -101.158168147Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158168147, -101.158168147}
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