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Simplifying x2 + 100x + -1200 = 0 Reorder the terms: -1200 + 100x + x2 = 0 Solving -1200 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 100x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 100x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 100x + x2 = 0 + 1200 100x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 100x + x2 = 1200 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 = 1200 + 2500 Reorder the terms: 2500 + 100x + x2 = 1200 + 2500 Combine like terms: 1200 + 2500 = 3700 2500 + 100x + x2 = 3700 Factor a perfect square on the left side: (x + 50)(x + 50) = 3700 Calculate the square root of the right side: 60.827625303 Break this problem into two subproblems by setting (x + 50) equal to 60.827625303 and -60.827625303.Subproblem 1
x + 50 = 60.827625303 Simplifying x + 50 = 60.827625303 Reorder the terms: 50 + x = 60.827625303 Solving 50 + x = 60.827625303 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 = 60.827625303 + -50 Combine like terms: 50 + -50 = 0 0 + x = 60.827625303 + -50 x = 60.827625303 + -50 Combine like terms: 60.827625303 + -50 = 10.827625303 x = 10.827625303 Simplifying x = 10.827625303Subproblem 2
x + 50 = -60.827625303 Simplifying x + 50 = -60.827625303 Reorder the terms: 50 + x = -60.827625303 Solving 50 + x = -60.827625303 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 = -60.827625303 + -50 Combine like terms: 50 + -50 = 0 0 + x = -60.827625303 + -50 x = -60.827625303 + -50 Combine like terms: -60.827625303 + -50 = -110.827625303 x = -110.827625303 Simplifying x = -110.827625303Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.827625303, -110.827625303}
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