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Simplifying x2 + 77.296552x + -13800 = 0 Reorder the terms: -13800 + 77.296552x + x2 = 0 Solving -13800 + 77.296552x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13800' to each side of the equation. -13800 + 77.296552x + 13800 + x2 = 0 + 13800 Reorder the terms: -13800 + 13800 + 77.296552x + x2 = 0 + 13800 Combine like terms: -13800 + 13800 = 0 0 + 77.296552x + x2 = 0 + 13800 77.296552x + x2 = 0 + 13800 Combine like terms: 0 + 13800 = 13800 77.296552x + x2 = 13800 The x term is 77.296552x. Take half its coefficient (38.648276). Square it (1493.689238) and add it to both sides. Add '1493.689238' to each side of the equation. 77.296552x + 1493.689238 + x2 = 13800 + 1493.689238 Reorder the terms: 1493.689238 + 77.296552x + x2 = 13800 + 1493.689238 Combine like terms: 13800 + 1493.689238 = 15293.689238 1493.689238 + 77.296552x + x2 = 15293.689238 Factor a perfect square on the left side: (x + 38.648276)(x + 38.648276) = 15293.689238 Calculate the square root of the right side: 123.667656394 Break this problem into two subproblems by setting (x + 38.648276) equal to 123.667656394 and -123.667656394.Subproblem 1
x + 38.648276 = 123.667656394 Simplifying x + 38.648276 = 123.667656394 Reorder the terms: 38.648276 + x = 123.667656394 Solving 38.648276 + x = 123.667656394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38.648276' to each side of the equation. 38.648276 + -38.648276 + x = 123.667656394 + -38.648276 Combine like terms: 38.648276 + -38.648276 = 0.000000 0.000000 + x = 123.667656394 + -38.648276 x = 123.667656394 + -38.648276 Combine like terms: 123.667656394 + -38.648276 = 85.019380394 x = 85.019380394 Simplifying x = 85.019380394Subproblem 2
x + 38.648276 = -123.667656394 Simplifying x + 38.648276 = -123.667656394 Reorder the terms: 38.648276 + x = -123.667656394 Solving 38.648276 + x = -123.667656394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38.648276' to each side of the equation. 38.648276 + -38.648276 + x = -123.667656394 + -38.648276 Combine like terms: 38.648276 + -38.648276 = 0.000000 0.000000 + x = -123.667656394 + -38.648276 x = -123.667656394 + -38.648276 Combine like terms: -123.667656394 + -38.648276 = -162.315932394 x = -162.315932394 Simplifying x = -162.315932394Solution
The solution to the problem is based on the solutions from the subproblems. x = {85.019380394, -162.315932394}
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