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Simplifying -1x2 + -16x + 64 = 0 Reorder the terms: 64 + -16x + -1x2 = 0 Solving 64 + -16x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 16x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 16x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 16x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 16x + x2 = 0 + 64 16x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 16x + x2 = 64 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 64 + 64 Reorder the terms: 64 + 16x + x2 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + 16x + x2 = 128 Factor a perfect square on the left side: (x + 8)(x + 8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + 8) equal to 11.313708499 and -11.313708499.Subproblem 1
x + 8 = 11.313708499 Simplifying x + 8 = 11.313708499 Reorder the terms: 8 + x = 11.313708499 Solving 8 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.313708499 + -8 x = 11.313708499 + -8 Combine like terms: 11.313708499 + -8 = 3.313708499 x = 3.313708499 Simplifying x = 3.313708499Subproblem 2
x + 8 = -11.313708499 Simplifying x + 8 = -11.313708499 Reorder the terms: 8 + x = -11.313708499 Solving 8 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.313708499 + -8 x = -11.313708499 + -8 Combine like terms: -11.313708499 + -8 = -19.313708499 x = -19.313708499 Simplifying x = -19.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.313708499, -19.313708499}
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