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Simplifying (27 * 27) + x2 + 54x + (64 * 64) + x2 + 128x = 34 * 34 Multiply 27 * 27 (729) + x2 + 54x + (64 * 64) + x2 + 128x = 34 * 34 729 + x2 + 54x + (64 * 64) + x2 + 128x = 34 * 34 Multiply 64 * 64 729 + x2 + 54x + (4096) + x2 + 128x = 34 * 34 729 + x2 + 54x + 4096 + x2 + 128x = 34 * 34 Reorder the terms: 729 + 4096 + 54x + 128x + x2 + x2 = 34 * 34 Combine like terms: 729 + 4096 = 4825 4825 + 54x + 128x + x2 + x2 = 34 * 34 Combine like terms: 54x + 128x = 182x 4825 + 182x + x2 + x2 = 34 * 34 Combine like terms: x2 + x2 = 2x2 4825 + 182x + 2x2 = 34 * 34 Multiply 34 * 34 4825 + 182x + 2x2 = 1156 Solving 4825 + 182x + 2x2 = 1156 Solving for variable 'x'. Reorder the terms: 4825 + -1156 + 182x + 2x2 = 1156 + -1156 Combine like terms: 4825 + -1156 = 3669 3669 + 182x + 2x2 = 1156 + -1156 Combine like terms: 1156 + -1156 = 0 3669 + 182x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1834.5 + 91x + x2 = 0 Move the constant term to the right: Add '-1834.5' to each side of the equation. 1834.5 + 91x + -1834.5 + x2 = 0 + -1834.5 Reorder the terms: 1834.5 + -1834.5 + 91x + x2 = 0 + -1834.5 Combine like terms: 1834.5 + -1834.5 = 0.0 0.0 + 91x + x2 = 0 + -1834.5 91x + x2 = 0 + -1834.5 Combine like terms: 0 + -1834.5 = -1834.5 91x + x2 = -1834.5 The x term is 91x. Take half its coefficient (45.5). Square it (2070.25) and add it to both sides. Add '2070.25' to each side of the equation. 91x + 2070.25 + x2 = -1834.5 + 2070.25 Reorder the terms: 2070.25 + 91x + x2 = -1834.5 + 2070.25 Combine like terms: -1834.5 + 2070.25 = 235.75 2070.25 + 91x + x2 = 235.75 Factor a perfect square on the left side: (x + 45.5)(x + 45.5) = 235.75 Calculate the square root of the right side: 15.354152533 Break this problem into two subproblems by setting (x + 45.5) equal to 15.354152533 and -15.354152533.Subproblem 1
x + 45.5 = 15.354152533 Simplifying x + 45.5 = 15.354152533 Reorder the terms: 45.5 + x = 15.354152533 Solving 45.5 + x = 15.354152533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.5' to each side of the equation. 45.5 + -45.5 + x = 15.354152533 + -45.5 Combine like terms: 45.5 + -45.5 = 0.0 0.0 + x = 15.354152533 + -45.5 x = 15.354152533 + -45.5 Combine like terms: 15.354152533 + -45.5 = -30.145847467 x = -30.145847467 Simplifying x = -30.145847467Subproblem 2
x + 45.5 = -15.354152533 Simplifying x + 45.5 = -15.354152533 Reorder the terms: 45.5 + x = -15.354152533 Solving 45.5 + x = -15.354152533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.5' to each side of the equation. 45.5 + -45.5 + x = -15.354152533 + -45.5 Combine like terms: 45.5 + -45.5 = 0.0 0.0 + x = -15.354152533 + -45.5 x = -15.354152533 + -45.5 Combine like terms: -15.354152533 + -45.5 = -60.854152533 x = -60.854152533 Simplifying x = -60.854152533Solution
The solution to the problem is based on the solutions from the subproblems. x = {-30.145847467, -60.854152533}
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