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Simplifying x2 + -100x = 2500 Reorder the terms: -100x + x2 = 2500 Solving -100x + x2 = 2500 Solving for variable 'x'. Reorder the terms: -2500 + -100x + x2 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -2500 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2500' to each side of the equation. -2500 + -100x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + -100x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + -100x + x2 = 0 + 2500 -100x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 -100x + x2 = 2500 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 = 2500 + 2500 Reorder the terms: 2500 + -100x + x2 = 2500 + 2500 Combine like terms: 2500 + 2500 = 5000 2500 + -100x + x2 = 5000 Factor a perfect square on the left side: (x + -50)(x + -50) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x + -50) equal to 70.710678119 and -70.710678119.Subproblem 1
x + -50 = 70.710678119 Simplifying x + -50 = 70.710678119 Reorder the terms: -50 + x = 70.710678119 Solving -50 + x = 70.710678119 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 = 70.710678119 + 50 Combine like terms: -50 + 50 = 0 0 + x = 70.710678119 + 50 x = 70.710678119 + 50 Combine like terms: 70.710678119 + 50 = 120.710678119 x = 120.710678119 Simplifying x = 120.710678119Subproblem 2
x + -50 = -70.710678119 Simplifying x + -50 = -70.710678119 Reorder the terms: -50 + x = -70.710678119 Solving -50 + x = -70.710678119 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 = -70.710678119 + 50 Combine like terms: -50 + 50 = 0 0 + x = -70.710678119 + 50 x = -70.710678119 + 50 Combine like terms: -70.710678119 + 50 = -20.710678119 x = -20.710678119 Simplifying x = -20.710678119Solution
The solution to the problem is based on the solutions from the subproblems. x = {120.710678119, -20.710678119}
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