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Simplifying x2 + 100x + -500 = 0 Reorder the terms: -500 + 100x + x2 = 0 Solving -500 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 100x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 100x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 100x + x2 = 0 + 500 100x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 100x + x2 = 500 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 = 500 + 2500 Reorder the terms: 2500 + 100x + x2 = 500 + 2500 Combine like terms: 500 + 2500 = 3000 2500 + 100x + x2 = 3000 Factor a perfect square on the left side: (x + 50)(x + 50) = 3000 Calculate the square root of the right side: 54.772255751 Break this problem into two subproblems by setting (x + 50) equal to 54.772255751 and -54.772255751.Subproblem 1
x + 50 = 54.772255751 Simplifying x + 50 = 54.772255751 Reorder the terms: 50 + x = 54.772255751 Solving 50 + x = 54.772255751 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 = 54.772255751 + -50 Combine like terms: 50 + -50 = 0 0 + x = 54.772255751 + -50 x = 54.772255751 + -50 Combine like terms: 54.772255751 + -50 = 4.772255751 x = 4.772255751 Simplifying x = 4.772255751Subproblem 2
x + 50 = -54.772255751 Simplifying x + 50 = -54.772255751 Reorder the terms: 50 + x = -54.772255751 Solving 50 + x = -54.772255751 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 = -54.772255751 + -50 Combine like terms: 50 + -50 = 0 0 + x = -54.772255751 + -50 x = -54.772255751 + -50 Combine like terms: -54.772255751 + -50 = -104.772255751 x = -104.772255751 Simplifying x = -104.772255751Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.772255751, -104.772255751}
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