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Simplifying x2 + -27x + 1 = 0 Reorder the terms: 1 + -27x + x2 = 0 Solving 1 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -27x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -27x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -27x + x2 = 0 + -1 -27x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -27x + x2 = -1 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 = -1 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -1 + 182.25 Combine like terms: -1 + 182.25 = 181.25 182.25 + -27x + x2 = 181.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (x + -13.5) equal to 13.462912018 and -13.462912018.Subproblem 1
x + -13.5 = 13.462912018 Simplifying x + -13.5 = 13.462912018 Reorder the terms: -13.5 + x = 13.462912018 Solving -13.5 + x = 13.462912018 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 = 13.462912018 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.462912018 + 13.5 x = 13.462912018 + 13.5 Combine like terms: 13.462912018 + 13.5 = 26.962912018 x = 26.962912018 Simplifying x = 26.962912018Subproblem 2
x + -13.5 = -13.462912018 Simplifying x + -13.5 = -13.462912018 Reorder the terms: -13.5 + x = -13.462912018 Solving -13.5 + x = -13.462912018 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 = -13.462912018 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.462912018 + 13.5 x = -13.462912018 + 13.5 Combine like terms: -13.462912018 + 13.5 = 0.037087982 x = 0.037087982 Simplifying x = 0.037087982Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.962912018, 0.037087982}
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