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Simplifying x2 + -27x + 169 = 0 Reorder the terms: 169 + -27x + x2 = 0 Solving 169 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-169' to each side of the equation. 169 + -27x + -169 + x2 = 0 + -169 Reorder the terms: 169 + -169 + -27x + x2 = 0 + -169 Combine like terms: 169 + -169 = 0 0 + -27x + x2 = 0 + -169 -27x + x2 = 0 + -169 Combine like terms: 0 + -169 = -169 -27x + x2 = -169 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 = -169 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -169 + 182.25 Combine like terms: -169 + 182.25 = 13.25 182.25 + -27x + x2 = 13.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -13.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -13.5 = 3.640054945 Simplifying x + -13.5 = 3.640054945 Reorder the terms: -13.5 + x = 3.640054945 Solving -13.5 + x = 3.640054945 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 = 3.640054945 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 3.640054945 + 13.5 x = 3.640054945 + 13.5 Combine like terms: 3.640054945 + 13.5 = 17.140054945 x = 17.140054945 Simplifying x = 17.140054945Subproblem 2
x + -13.5 = -3.640054945 Simplifying x + -13.5 = -3.640054945 Reorder the terms: -13.5 + x = -3.640054945 Solving -13.5 + x = -3.640054945 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 = -3.640054945 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -3.640054945 + 13.5 x = -3.640054945 + 13.5 Combine like terms: -3.640054945 + 13.5 = 9.859945055 x = 9.859945055 Simplifying x = 9.859945055Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.140054945, 9.859945055}
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