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Simplifying 54 = 27x + -1x2 Solving 54 = 27x + -1x2 Solving for variable 'x'. Reorder the terms: 54 + -27x + x2 = 27x + -27x + -1x2 + x2 Combine like terms: 27x + -27x = 0 54 + -27x + x2 = 0 + -1x2 + x2 54 + -27x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 54 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -27x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -27x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -27x + x2 = 0 + -54 -27x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -27x + x2 = -54 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 = -54 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -54 + 182.25 Combine like terms: -54 + 182.25 = 128.25 182.25 + -27x + x2 = 128.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + -13.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + -13.5 = 11.324751653 Simplifying x + -13.5 = 11.324751653 Reorder the terms: -13.5 + x = 11.324751653 Solving -13.5 + x = 11.324751653 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 = 11.324751653 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 11.324751653 + 13.5 x = 11.324751653 + 13.5 Combine like terms: 11.324751653 + 13.5 = 24.824751653 x = 24.824751653 Simplifying x = 24.824751653Subproblem 2
x + -13.5 = -11.324751653 Simplifying x + -13.5 = -11.324751653 Reorder the terms: -13.5 + x = -11.324751653 Solving -13.5 + x = -11.324751653 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 = -11.324751653 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -11.324751653 + 13.5 x = -11.324751653 + 13.5 Combine like terms: -11.324751653 + 13.5 = 2.175248347 x = 2.175248347 Simplifying x = 2.175248347Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.824751653, 2.175248347}
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