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Simplifying x2 + -54x + 180 = 0 Reorder the terms: 180 + -54x + x2 = 0 Solving 180 + -54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -54x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -54x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -54x + x2 = 0 + -180 -54x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -54x + x2 = -180 The x term is -54x. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54x + 729 + x2 = -180 + 729 Reorder the terms: 729 + -54x + x2 = -180 + 729 Combine like terms: -180 + 729 = 549 729 + -54x + x2 = 549 Factor a perfect square on the left side: (x + -27)(x + -27) = 549 Calculate the square root of the right side: 23.430749028 Break this problem into two subproblems by setting (x + -27) equal to 23.430749028 and -23.430749028.Subproblem 1
x + -27 = 23.430749028 Simplifying x + -27 = 23.430749028 Reorder the terms: -27 + x = 23.430749028 Solving -27 + x = 23.430749028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = 23.430749028 + 27 Combine like terms: -27 + 27 = 0 0 + x = 23.430749028 + 27 x = 23.430749028 + 27 Combine like terms: 23.430749028 + 27 = 50.430749028 x = 50.430749028 Simplifying x = 50.430749028Subproblem 2
x + -27 = -23.430749028 Simplifying x + -27 = -23.430749028 Reorder the terms: -27 + x = -23.430749028 Solving -27 + x = -23.430749028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = -23.430749028 + 27 Combine like terms: -27 + 27 = 0 0 + x = -23.430749028 + 27 x = -23.430749028 + 27 Combine like terms: -23.430749028 + 27 = 3.569250972 x = 3.569250972 Simplifying x = 3.569250972Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.430749028, 3.569250972}
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