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Simplifying x2 + 100x + 2 = 0 Reorder the terms: 2 + 100x + x2 = 0 Solving 2 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 100x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 100x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 100x + x2 = 0 + -2 100x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 100x + x2 = -2 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 = -2 + 2500 Reorder the terms: 2500 + 100x + x2 = -2 + 2500 Combine like terms: -2 + 2500 = 2498 2500 + 100x + x2 = 2498 Factor a perfect square on the left side: (x + 50)(x + 50) = 2498 Calculate the square root of the right side: 49.979995998 Break this problem into two subproblems by setting (x + 50) equal to 49.979995998 and -49.979995998.Subproblem 1
x + 50 = 49.979995998 Simplifying x + 50 = 49.979995998 Reorder the terms: 50 + x = 49.979995998 Solving 50 + x = 49.979995998 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 = 49.979995998 + -50 Combine like terms: 50 + -50 = 0 0 + x = 49.979995998 + -50 x = 49.979995998 + -50 Combine like terms: 49.979995998 + -50 = -0.020004002 x = -0.020004002 Simplifying x = -0.020004002Subproblem 2
x + 50 = -49.979995998 Simplifying x + 50 = -49.979995998 Reorder the terms: 50 + x = -49.979995998 Solving 50 + x = -49.979995998 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 = -49.979995998 + -50 Combine like terms: 50 + -50 = 0 0 + x = -49.979995998 + -50 x = -49.979995998 + -50 Combine like terms: -49.979995998 + -50 = -99.979995998 x = -99.979995998 Simplifying x = -99.979995998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.020004002, -99.979995998}
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