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Simplifying x2 + 92x + -912 = 0 Reorder the terms: -912 + 92x + x2 = 0 Solving -912 + 92x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '912' to each side of the equation. -912 + 92x + 912 + x2 = 0 + 912 Reorder the terms: -912 + 912 + 92x + x2 = 0 + 912 Combine like terms: -912 + 912 = 0 0 + 92x + x2 = 0 + 912 92x + x2 = 0 + 912 Combine like terms: 0 + 912 = 912 92x + x2 = 912 The x term is 92x. Take half its coefficient (46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. 92x + 2116 + x2 = 912 + 2116 Reorder the terms: 2116 + 92x + x2 = 912 + 2116 Combine like terms: 912 + 2116 = 3028 2116 + 92x + x2 = 3028 Factor a perfect square on the left side: (x + 46)(x + 46) = 3028 Calculate the square root of the right side: 55.027265969 Break this problem into two subproblems by setting (x + 46) equal to 55.027265969 and -55.027265969.Subproblem 1
x + 46 = 55.027265969 Simplifying x + 46 = 55.027265969 Reorder the terms: 46 + x = 55.027265969 Solving 46 + x = 55.027265969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = 55.027265969 + -46 Combine like terms: 46 + -46 = 0 0 + x = 55.027265969 + -46 x = 55.027265969 + -46 Combine like terms: 55.027265969 + -46 = 9.027265969 x = 9.027265969 Simplifying x = 9.027265969Subproblem 2
x + 46 = -55.027265969 Simplifying x + 46 = -55.027265969 Reorder the terms: 46 + x = -55.027265969 Solving 46 + x = -55.027265969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = -55.027265969 + -46 Combine like terms: 46 + -46 = 0 0 + x = -55.027265969 + -46 x = -55.027265969 + -46 Combine like terms: -55.027265969 + -46 = -101.027265969 x = -101.027265969 Simplifying x = -101.027265969Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.027265969, -101.027265969}
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