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Simplifying x2 = 100x + 200 Reorder the terms: x2 = 200 + 100x Solving x2 = 200 + 100x Solving for variable 'x'. Reorder the terms: -200 + -100x + x2 = 200 + 100x + -200 + -100x Reorder the terms: -200 + -100x + x2 = 200 + -200 + 100x + -100x Combine like terms: 200 + -200 = 0 -200 + -100x + x2 = 0 + 100x + -100x -200 + -100x + x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -200 + -100x + x2 = 0 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 = 101.961524227 x = 101.961524227 Simplifying x = 101.961524227Subproblem 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 = -1.961524227 x = -1.961524227 Simplifying x = -1.961524227Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.961524227, -1.961524227}
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