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Simplifying x2 + -100x + -50 = 0 Reorder the terms: -50 + -100x + x2 = 0 Solving -50 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -100x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -100x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -100x + x2 = 0 + 50 -100x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -100x + x2 = 50 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 = 50 + 2500 Reorder the terms: 2500 + -100x + x2 = 50 + 2500 Combine like terms: 50 + 2500 = 2550 2500 + -100x + x2 = 2550 Factor a perfect square on the left side: (x + -50)(x + -50) = 2550 Calculate the square root of the right side: 50.497524692 Break this problem into two subproblems by setting (x + -50) equal to 50.497524692 and -50.497524692.Subproblem 1
x + -50 = 50.497524692 Simplifying x + -50 = 50.497524692 Reorder the terms: -50 + x = 50.497524692 Solving -50 + x = 50.497524692 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 = 50.497524692 + 50 Combine like terms: -50 + 50 = 0 0 + x = 50.497524692 + 50 x = 50.497524692 + 50 Combine like terms: 50.497524692 + 50 = 100.497524692 x = 100.497524692 Simplifying x = 100.497524692Subproblem 2
x + -50 = -50.497524692 Simplifying x + -50 = -50.497524692 Reorder the terms: -50 + x = -50.497524692 Solving -50 + x = -50.497524692 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 = -50.497524692 + 50 Combine like terms: -50 + 50 = 0 0 + x = -50.497524692 + 50 x = -50.497524692 + 50 Combine like terms: -50.497524692 + 50 = -0.497524692 x = -0.497524692 Simplifying x = -0.497524692Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.497524692, -0.497524692}
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