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Simplifying x2 + 55x + 2 = 0 Reorder the terms: 2 + 55x + x2 = 0 Solving 2 + 55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 55x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 55x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 55x + x2 = 0 + -2 55x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 55x + x2 = -2 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 = -2 + 756.25 Reorder the terms: 756.25 + 55x + x2 = -2 + 756.25 Combine like terms: -2 + 756.25 = 754.25 756.25 + 55x + x2 = 754.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 754.25 Calculate the square root of the right side: 27.46361229 Break this problem into two subproblems by setting (x + 27.5) equal to 27.46361229 and -27.46361229.Subproblem 1
x + 27.5 = 27.46361229 Simplifying x + 27.5 = 27.46361229 Reorder the terms: 27.5 + x = 27.46361229 Solving 27.5 + x = 27.46361229 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 = 27.46361229 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 27.46361229 + -27.5 x = 27.46361229 + -27.5 Combine like terms: 27.46361229 + -27.5 = -0.03638771 x = -0.03638771 Simplifying x = -0.03638771Subproblem 2
x + 27.5 = -27.46361229 Simplifying x + 27.5 = -27.46361229 Reorder the terms: 27.5 + x = -27.46361229 Solving 27.5 + x = -27.46361229 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 = -27.46361229 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -27.46361229 + -27.5 x = -27.46361229 + -27.5 Combine like terms: -27.46361229 + -27.5 = -54.96361229 x = -54.96361229 Simplifying x = -54.96361229Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.03638771, -54.96361229}
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