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Simplifying 2x2 + -54x + -225 = 0 Reorder the terms: -225 + -54x + 2x2 = 0 Solving -225 + -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'. -112.5 + -27x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + -27x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + -27x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + -27x + x2 = 0 + 112.5 -27x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 -27x + x2 = 112.5 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 = 112.5 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 112.5 + 182.25 Combine like terms: 112.5 + 182.25 = 294.75 182.25 + -27x + x2 = 294.75 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 294.75 Calculate the square root of the right side: 17.168284713 Break this problem into two subproblems by setting (x + -13.5) equal to 17.168284713 and -17.168284713.Subproblem 1
x + -13.5 = 17.168284713 Simplifying x + -13.5 = 17.168284713 Reorder the terms: -13.5 + x = 17.168284713 Solving -13.5 + x = 17.168284713 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 = 17.168284713 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 17.168284713 + 13.5 x = 17.168284713 + 13.5 Combine like terms: 17.168284713 + 13.5 = 30.668284713 x = 30.668284713 Simplifying x = 30.668284713Subproblem 2
x + -13.5 = -17.168284713 Simplifying x + -13.5 = -17.168284713 Reorder the terms: -13.5 + x = -17.168284713 Solving -13.5 + x = -17.168284713 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 = -17.168284713 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -17.168284713 + 13.5 x = -17.168284713 + 13.5 Combine like terms: -17.168284713 + 13.5 = -3.668284713 x = -3.668284713 Simplifying x = -3.668284713Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.668284713, -3.668284713}
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