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Simplifying 2x2 + -200x + -225 = 0 Reorder the terms: -225 + -200x + 2x2 = 0 Solving -225 + -200x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112.5 + -100x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + -100x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + -100x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + -100x + x2 = 0 + 112.5 -100x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 -100x + x2 = 112.5 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 = 112.5 + 2500 Reorder the terms: 2500 + -100x + x2 = 112.5 + 2500 Combine like terms: 112.5 + 2500 = 2612.5 2500 + -100x + x2 = 2612.5 Factor a perfect square on the left side: (x + -50)(x + -50) = 2612.5 Calculate the square root of the right side: 51.112620751 Break this problem into two subproblems by setting (x + -50) equal to 51.112620751 and -51.112620751.Subproblem 1
x + -50 = 51.112620751 Simplifying x + -50 = 51.112620751 Reorder the terms: -50 + x = 51.112620751 Solving -50 + x = 51.112620751 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 = 51.112620751 + 50 Combine like terms: -50 + 50 = 0 0 + x = 51.112620751 + 50 x = 51.112620751 + 50 Combine like terms: 51.112620751 + 50 = 101.112620751 x = 101.112620751 Simplifying x = 101.112620751Subproblem 2
x + -50 = -51.112620751 Simplifying x + -50 = -51.112620751 Reorder the terms: -50 + x = -51.112620751 Solving -50 + x = -51.112620751 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 = -51.112620751 + 50 Combine like terms: -50 + 50 = 0 0 + x = -51.112620751 + 50 x = -51.112620751 + 50 Combine like terms: -51.112620751 + 50 = -1.112620751 x = -1.112620751 Simplifying x = -1.112620751Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.112620751, -1.112620751}
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