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Simplifying x2 + 92x + -9 = 0 Reorder the terms: -9 + 92x + x2 = 0 Solving -9 + 92x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 92x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 92x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 92x + x2 = 0 + 9 92x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 92x + x2 = 9 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 = 9 + 2116 Reorder the terms: 2116 + 92x + x2 = 9 + 2116 Combine like terms: 9 + 2116 = 2125 2116 + 92x + x2 = 2125 Factor a perfect square on the left side: (x + 46)(x + 46) = 2125 Calculate the square root of the right side: 46.097722286 Break this problem into two subproblems by setting (x + 46) equal to 46.097722286 and -46.097722286.Subproblem 1
x + 46 = 46.097722286 Simplifying x + 46 = 46.097722286 Reorder the terms: 46 + x = 46.097722286 Solving 46 + x = 46.097722286 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 = 46.097722286 + -46 Combine like terms: 46 + -46 = 0 0 + x = 46.097722286 + -46 x = 46.097722286 + -46 Combine like terms: 46.097722286 + -46 = 0.097722286 x = 0.097722286 Simplifying x = 0.097722286Subproblem 2
x + 46 = -46.097722286 Simplifying x + 46 = -46.097722286 Reorder the terms: 46 + x = -46.097722286 Solving 46 + x = -46.097722286 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 = -46.097722286 + -46 Combine like terms: 46 + -46 = 0 0 + x = -46.097722286 + -46 x = -46.097722286 + -46 Combine like terms: -46.097722286 + -46 = -92.097722286 x = -92.097722286 Simplifying x = -92.097722286Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.097722286, -92.097722286}
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