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Simplifying x2 + -246x = -144 Reorder the terms: -246x + x2 = -144 Solving -246x + x2 = -144 Solving for variable 'x'. Reorder the terms: 144 + -246x + x2 = -144 + 144 Combine like terms: -144 + 144 = 0 144 + -246x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -246x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -246x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -246x + x2 = 0 + -144 -246x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -246x + x2 = -144 The x term is -246x. Take half its coefficient (-123). Square it (15129) and add it to both sides. Add '15129' to each side of the equation. -246x + 15129 + x2 = -144 + 15129 Reorder the terms: 15129 + -246x + x2 = -144 + 15129 Combine like terms: -144 + 15129 = 14985 15129 + -246x + x2 = 14985 Factor a perfect square on the left side: (x + -123)(x + -123) = 14985 Calculate the square root of the right side: 122.413234579 Break this problem into two subproblems by setting (x + -123) equal to 122.413234579 and -122.413234579.Subproblem 1
x + -123 = 122.413234579 Simplifying x + -123 = 122.413234579 Reorder the terms: -123 + x = 122.413234579 Solving -123 + x = 122.413234579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '123' to each side of the equation. -123 + 123 + x = 122.413234579 + 123 Combine like terms: -123 + 123 = 0 0 + x = 122.413234579 + 123 x = 122.413234579 + 123 Combine like terms: 122.413234579 + 123 = 245.413234579 x = 245.413234579 Simplifying x = 245.413234579Subproblem 2
x + -123 = -122.413234579 Simplifying x + -123 = -122.413234579 Reorder the terms: -123 + x = -122.413234579 Solving -123 + x = -122.413234579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '123' to each side of the equation. -123 + 123 + x = -122.413234579 + 123 Combine like terms: -123 + 123 = 0 0 + x = -122.413234579 + 123 x = -122.413234579 + 123 Combine like terms: -122.413234579 + 123 = 0.586765421 x = 0.586765421 Simplifying x = 0.586765421Solution
The solution to the problem is based on the solutions from the subproblems. x = {245.413234579, 0.586765421}
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