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Simplifying x2 + -54x + 12 = 0 Reorder the terms: 12 + -54x + x2 = 0 Solving 12 + -54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -54x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -54x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -54x + x2 = 0 + -12 -54x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -54x + x2 = -12 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 = -12 + 729 Reorder the terms: 729 + -54x + x2 = -12 + 729 Combine like terms: -12 + 729 = 717 729 + -54x + x2 = 717 Factor a perfect square on the left side: (x + -27)(x + -27) = 717 Calculate the square root of the right side: 26.776855678 Break this problem into two subproblems by setting (x + -27) equal to 26.776855678 and -26.776855678.Subproblem 1
x + -27 = 26.776855678 Simplifying x + -27 = 26.776855678 Reorder the terms: -27 + x = 26.776855678 Solving -27 + x = 26.776855678 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 = 26.776855678 + 27 Combine like terms: -27 + 27 = 0 0 + x = 26.776855678 + 27 x = 26.776855678 + 27 Combine like terms: 26.776855678 + 27 = 53.776855678 x = 53.776855678 Simplifying x = 53.776855678Subproblem 2
x + -27 = -26.776855678 Simplifying x + -27 = -26.776855678 Reorder the terms: -27 + x = -26.776855678 Solving -27 + x = -26.776855678 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 = -26.776855678 + 27 Combine like terms: -27 + 27 = 0 0 + x = -26.776855678 + 27 x = -26.776855678 + 27 Combine like terms: -26.776855678 + 27 = 0.223144322 x = 0.223144322 Simplifying x = 0.223144322Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.776855678, 0.223144322}
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