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Simplifying x2 + -54x + 225 = 0 Reorder the terms: 225 + -54x + x2 = 0 Solving 225 + -54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + -54x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -54x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -54x + x2 = 0 + -225 -54x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -54x + x2 = -225 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 = -225 + 729 Reorder the terms: 729 + -54x + x2 = -225 + 729 Combine like terms: -225 + 729 = 504 729 + -54x + x2 = 504 Factor a perfect square on the left side: (x + -27)(x + -27) = 504 Calculate the square root of the right side: 22.449944321 Break this problem into two subproblems by setting (x + -27) equal to 22.449944321 and -22.449944321.Subproblem 1
x + -27 = 22.449944321 Simplifying x + -27 = 22.449944321 Reorder the terms: -27 + x = 22.449944321 Solving -27 + x = 22.449944321 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 = 22.449944321 + 27 Combine like terms: -27 + 27 = 0 0 + x = 22.449944321 + 27 x = 22.449944321 + 27 Combine like terms: 22.449944321 + 27 = 49.449944321 x = 49.449944321 Simplifying x = 49.449944321Subproblem 2
x + -27 = -22.449944321 Simplifying x + -27 = -22.449944321 Reorder the terms: -27 + x = -22.449944321 Solving -27 + x = -22.449944321 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 = -22.449944321 + 27 Combine like terms: -27 + 27 = 0 0 + x = -22.449944321 + 27 x = -22.449944321 + 27 Combine like terms: -22.449944321 + 27 = 4.550055679 x = 4.550055679 Simplifying x = 4.550055679Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.449944321, 4.550055679}
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