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Simplifying -1x2 + -16x + 39 = 0 Reorder the terms: 39 + -16x + -1x2 = 0 Solving 39 + -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'. -39 + 16x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 16x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 16x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 16x + x2 = 0 + 39 16x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 16x + x2 = 39 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 = 39 + 64 Reorder the terms: 64 + 16x + x2 = 39 + 64 Combine like terms: 39 + 64 = 103 64 + 16x + x2 = 103 Factor a perfect square on the left side: (x + 8)(x + 8) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + 8) equal to 10.148891565 and -10.148891565.Subproblem 1
x + 8 = 10.148891565 Simplifying x + 8 = 10.148891565 Reorder the terms: 8 + x = 10.148891565 Solving 8 + x = 10.148891565 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 = 10.148891565 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.148891565 + -8 x = 10.148891565 + -8 Combine like terms: 10.148891565 + -8 = 2.148891565 x = 2.148891565 Simplifying x = 2.148891565Subproblem 2
x + 8 = -10.148891565 Simplifying x + 8 = -10.148891565 Reorder the terms: 8 + x = -10.148891565 Solving 8 + x = -10.148891565 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 = -10.148891565 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.148891565 + -8 x = -10.148891565 + -8 Combine like terms: -10.148891565 + -8 = -18.148891565 x = -18.148891565 Simplifying x = -18.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.148891565, -18.148891565}
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