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Simplifying x2 + 55x + -20 = 0 Reorder the terms: -20 + 55x + x2 = 0 Solving -20 + 55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 55x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 55x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 55x + x2 = 0 + 20 55x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 55x + x2 = 20 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 = 20 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 20 + 756.25 Combine like terms: 20 + 756.25 = 776.25 756.25 + 55x + x2 = 776.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 776.25 Calculate the square root of the right side: 27.861263432 Break this problem into two subproblems by setting (x + 27.5) equal to 27.861263432 and -27.861263432.Subproblem 1
x + 27.5 = 27.861263432 Simplifying x + 27.5 = 27.861263432 Reorder the terms: 27.5 + x = 27.861263432 Solving 27.5 + x = 27.861263432 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 = 27.861263432 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 27.861263432 + -27.5 x = 27.861263432 + -27.5 Combine like terms: 27.861263432 + -27.5 = 0.361263432 x = 0.361263432 Simplifying x = 0.361263432Subproblem 2
x + 27.5 = -27.861263432 Simplifying x + 27.5 = -27.861263432 Reorder the terms: 27.5 + x = -27.861263432 Solving 27.5 + x = -27.861263432 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 = -27.861263432 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -27.861263432 + -27.5 x = -27.861263432 + -27.5 Combine like terms: -27.861263432 + -27.5 = -55.361263432 x = -55.361263432 Simplifying x = -55.361263432Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.361263432, -55.361263432}
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