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Simplifying x2 + -27x + 52 = 0 Reorder the terms: 52 + -27x + x2 = 0 Solving 52 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -27x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -27x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -27x + x2 = 0 + -52 -27x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -27x + x2 = -52 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -52 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -52 + 182.25 Combine like terms: -52 + 182.25 = 130.25 182.25 + -27x + x2 = 130.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + -13.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + -13.5 = 11.412712211 Simplifying x + -13.5 = 11.412712211 Reorder the terms: -13.5 + x = 11.412712211 Solving -13.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 11.412712211 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 11.412712211 + 13.5 x = 11.412712211 + 13.5 Combine like terms: 11.412712211 + 13.5 = 24.912712211 x = 24.912712211 Simplifying x = 24.912712211Subproblem 2
x + -13.5 = -11.412712211 Simplifying x + -13.5 = -11.412712211 Reorder the terms: -13.5 + x = -11.412712211 Solving -13.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -11.412712211 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -11.412712211 + 13.5 x = -11.412712211 + 13.5 Combine like terms: -11.412712211 + 13.5 = 2.087287789 x = 2.087287789 Simplifying x = 2.087287789Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.912712211, 2.087287789}
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