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Simplifying x2 + 27x + 124 = 0 Reorder the terms: 124 + 27x + x2 = 0 Solving 124 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + 27x + -124 + x2 = 0 + -124 Reorder the terms: 124 + -124 + 27x + x2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + 27x + x2 = 0 + -124 27x + x2 = 0 + -124 Combine like terms: 0 + -124 = -124 27x + x2 = -124 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 = -124 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -124 + 182.25 Combine like terms: -124 + 182.25 = 58.25 182.25 + 27x + x2 = 58.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 13.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 13.5 = 7.632168761 Simplifying x + 13.5 = 7.632168761 Reorder the terms: 13.5 + x = 7.632168761 Solving 13.5 + x = 7.632168761 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 = 7.632168761 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 7.632168761 + -13.5 x = 7.632168761 + -13.5 Combine like terms: 7.632168761 + -13.5 = -5.867831239 x = -5.867831239 Simplifying x = -5.867831239Subproblem 2
x + 13.5 = -7.632168761 Simplifying x + 13.5 = -7.632168761 Reorder the terms: 13.5 + x = -7.632168761 Solving 13.5 + x = -7.632168761 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 = -7.632168761 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -7.632168761 + -13.5 x = -7.632168761 + -13.5 Combine like terms: -7.632168761 + -13.5 = -21.132168761 x = -21.132168761 Simplifying x = -21.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.867831239, -21.132168761}
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