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Simplifying 2x2 + 54x + -13195 = 0 Reorder the terms: -13195 + 54x + 2x2 = 0 Solving -13195 + 54x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6597.5 + 27x + x2 = 0 Move the constant term to the right: Add '6597.5' to each side of the equation. -6597.5 + 27x + 6597.5 + x2 = 0 + 6597.5 Reorder the terms: -6597.5 + 6597.5 + 27x + x2 = 0 + 6597.5 Combine like terms: -6597.5 + 6597.5 = 0.0 0.0 + 27x + x2 = 0 + 6597.5 27x + x2 = 0 + 6597.5 Combine like terms: 0 + 6597.5 = 6597.5 27x + x2 = 6597.5 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 = 6597.5 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 6597.5 + 182.25 Combine like terms: 6597.5 + 182.25 = 6779.75 182.25 + 27x + x2 = 6779.75 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 6779.75 Calculate the square root of the right side: 82.339237305 Break this problem into two subproblems by setting (x + 13.5) equal to 82.339237305 and -82.339237305.Subproblem 1
x + 13.5 = 82.339237305 Simplifying x + 13.5 = 82.339237305 Reorder the terms: 13.5 + x = 82.339237305 Solving 13.5 + x = 82.339237305 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 = 82.339237305 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 82.339237305 + -13.5 x = 82.339237305 + -13.5 Combine like terms: 82.339237305 + -13.5 = 68.839237305 x = 68.839237305 Simplifying x = 68.839237305Subproblem 2
x + 13.5 = -82.339237305 Simplifying x + 13.5 = -82.339237305 Reorder the terms: 13.5 + x = -82.339237305 Solving 13.5 + x = -82.339237305 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 = -82.339237305 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -82.339237305 + -13.5 x = -82.339237305 + -13.5 Combine like terms: -82.339237305 + -13.5 = -95.839237305 x = -95.839237305 Simplifying x = -95.839237305Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.839237305, -95.839237305}
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