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Simplifying x2 + 100x + -200 = 0 Reorder the terms: -200 + 100x + x2 = 0 Solving -200 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 100x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 100x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 100x + x2 = 0 + 200 100x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 100x + x2 = 200 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 = 200 + 2500 Reorder the terms: 2500 + 100x + x2 = 200 + 2500 Combine like terms: 200 + 2500 = 2700 2500 + 100x + x2 = 2700 Factor a perfect square on the left side: (x + 50)(x + 50) = 2700 Calculate the square root of the right side: 51.961524227 Break this problem into two subproblems by setting (x + 50) equal to 51.961524227 and -51.961524227.Subproblem 1
x + 50 = 51.961524227 Simplifying x + 50 = 51.961524227 Reorder the terms: 50 + x = 51.961524227 Solving 50 + x = 51.961524227 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 = 51.961524227 + -50 Combine like terms: 50 + -50 = 0 0 + x = 51.961524227 + -50 x = 51.961524227 + -50 Combine like terms: 51.961524227 + -50 = 1.961524227 x = 1.961524227 Simplifying x = 1.961524227Subproblem 2
x + 50 = -51.961524227 Simplifying x + 50 = -51.961524227 Reorder the terms: 50 + x = -51.961524227 Solving 50 + x = -51.961524227 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 = -51.961524227 + -50 Combine like terms: 50 + -50 = 0 0 + x = -51.961524227 + -50 x = -51.961524227 + -50 Combine like terms: -51.961524227 + -50 = -101.961524227 x = -101.961524227 Simplifying x = -101.961524227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.961524227, -101.961524227}
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