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Simplifying x2 + 25x + -54 = 204 Reorder the terms: -54 + 25x + x2 = 204 Solving -54 + 25x + x2 = 204 Solving for variable 'x'. Reorder the terms: -54 + -204 + 25x + x2 = 204 + -204 Combine like terms: -54 + -204 = -258 -258 + 25x + x2 = 204 + -204 Combine like terms: 204 + -204 = 0 -258 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '258' to each side of the equation. -258 + 25x + 258 + x2 = 0 + 258 Reorder the terms: -258 + 258 + 25x + x2 = 0 + 258 Combine like terms: -258 + 258 = 0 0 + 25x + x2 = 0 + 258 25x + x2 = 0 + 258 Combine like terms: 0 + 258 = 258 25x + x2 = 258 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 258 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 258 + 156.25 Combine like terms: 258 + 156.25 = 414.25 156.25 + 25x + x2 = 414.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 414.25 Calculate the square root of the right side: 20.353132437 Break this problem into two subproblems by setting (x + 12.5) equal to 20.353132437 and -20.353132437.Subproblem 1
x + 12.5 = 20.353132437 Simplifying x + 12.5 = 20.353132437 Reorder the terms: 12.5 + x = 20.353132437 Solving 12.5 + x = 20.353132437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 20.353132437 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 20.353132437 + -12.5 x = 20.353132437 + -12.5 Combine like terms: 20.353132437 + -12.5 = 7.853132437 x = 7.853132437 Simplifying x = 7.853132437Subproblem 2
x + 12.5 = -20.353132437 Simplifying x + 12.5 = -20.353132437 Reorder the terms: 12.5 + x = -20.353132437 Solving 12.5 + x = -20.353132437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -20.353132437 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -20.353132437 + -12.5 x = -20.353132437 + -12.5 Combine like terms: -20.353132437 + -12.5 = -32.853132437 x = -32.853132437 Simplifying x = -32.853132437Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.853132437, -32.853132437}
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