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Simplifying x2 + 27x + 182 = 124 Reorder the terms: 182 + 27x + x2 = 124 Solving 182 + 27x + x2 = 124 Solving for variable 'x'. Reorder the terms: 182 + -124 + 27x + x2 = 124 + -124 Combine like terms: 182 + -124 = 58 58 + 27x + x2 = 124 + -124 Combine like terms: 124 + -124 = 0 58 + 27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + 27x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + 27x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + 27x + x2 = 0 + -58 27x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 27x + x2 = -58 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 = -58 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -58 + 182.25 Combine like terms: -58 + 182.25 = 124.25 182.25 + 27x + x2 = 124.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + 13.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + 13.5 = 11.146748405 Simplifying x + 13.5 = 11.146748405 Reorder the terms: 13.5 + x = 11.146748405 Solving 13.5 + x = 11.146748405 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 = 11.146748405 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 11.146748405 + -13.5 x = 11.146748405 + -13.5 Combine like terms: 11.146748405 + -13.5 = -2.353251595 x = -2.353251595 Simplifying x = -2.353251595Subproblem 2
x + 13.5 = -11.146748405 Simplifying x + 13.5 = -11.146748405 Reorder the terms: 13.5 + x = -11.146748405 Solving 13.5 + x = -11.146748405 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 = -11.146748405 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -11.146748405 + -13.5 x = -11.146748405 + -13.5 Combine like terms: -11.146748405 + -13.5 = -24.646748405 x = -24.646748405 Simplifying x = -24.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.353251595, -24.646748405}
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