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Simplifying x2 + 55x + -1100 = 0 Reorder the terms: -1100 + 55x + x2 = 0 Solving -1100 + 55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1100' to each side of the equation. -1100 + 55x + 1100 + x2 = 0 + 1100 Reorder the terms: -1100 + 1100 + 55x + x2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + 55x + x2 = 0 + 1100 55x + x2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 55x + x2 = 1100 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = 1100 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 1100 + 756.25 Combine like terms: 1100 + 756.25 = 1856.25 756.25 + 55x + x2 = 1856.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 1856.25 Calculate the square root of the right side: 43.084219849 Break this problem into two subproblems by setting (x + 27.5) equal to 43.084219849 and -43.084219849.Subproblem 1
x + 27.5 = 43.084219849 Simplifying x + 27.5 = 43.084219849 Reorder the terms: 27.5 + x = 43.084219849 Solving 27.5 + x = 43.084219849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 43.084219849 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 43.084219849 + -27.5 x = 43.084219849 + -27.5 Combine like terms: 43.084219849 + -27.5 = 15.584219849 x = 15.584219849 Simplifying x = 15.584219849Subproblem 2
x + 27.5 = -43.084219849 Simplifying x + 27.5 = -43.084219849 Reorder the terms: 27.5 + x = -43.084219849 Solving 27.5 + x = -43.084219849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -43.084219849 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -43.084219849 + -27.5 x = -43.084219849 + -27.5 Combine like terms: -43.084219849 + -27.5 = -70.584219849 x = -70.584219849 Simplifying x = -70.584219849Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.584219849, -70.584219849}
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