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Simplifying x2 + 27x + 53 = 0 Reorder the terms: 53 + 27x + x2 = 0 Solving 53 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 27x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 27x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 27x + x2 = 0 + -53 27x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 27x + x2 = -53 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 = -53 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -53 + 182.25 Combine like terms: -53 + 182.25 = 129.25 182.25 + 27x + x2 = 129.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + 13.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + 13.5 = 11.368817001 Simplifying x + 13.5 = 11.368817001 Reorder the terms: 13.5 + x = 11.368817001 Solving 13.5 + x = 11.368817001 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 = 11.368817001 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 11.368817001 + -13.5 x = 11.368817001 + -13.5 Combine like terms: 11.368817001 + -13.5 = -2.131182999 x = -2.131182999 Simplifying x = -2.131182999Subproblem 2
x + 13.5 = -11.368817001 Simplifying x + 13.5 = -11.368817001 Reorder the terms: 13.5 + x = -11.368817001 Solving 13.5 + x = -11.368817001 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 = -11.368817001 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -11.368817001 + -13.5 x = -11.368817001 + -13.5 Combine like terms: -11.368817001 + -13.5 = -24.868817001 x = -24.868817001 Simplifying x = -24.868817001Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.131182999, -24.868817001}
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