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Simplifying -16x2 + -1x + 144 = 0 Reorder the terms: 144 + -1x + -16x2 = 0 Solving 144 + -1x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -9 + 0.0625x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.0625x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 0.0625x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.0625x + x2 = 0 + 9 0.0625x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.0625x + x2 = 9 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 9 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 9 + 0.0009765625 Combine like terms: 9 + 0.0009765625 = 9.0009765625 0.0009765625 + 0.0625x + x2 = 9.0009765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 9.0009765625 Calculate the square root of the right side: 3.000162756 Break this problem into two subproblems by setting (x + 0.03125) equal to 3.000162756 and -3.000162756.Subproblem 1
x + 0.03125 = 3.000162756 Simplifying x + 0.03125 = 3.000162756 Reorder the terms: 0.03125 + x = 3.000162756 Solving 0.03125 + x = 3.000162756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 3.000162756 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 3.000162756 + -0.03125 x = 3.000162756 + -0.03125 Combine like terms: 3.000162756 + -0.03125 = 2.968912756 x = 2.968912756 Simplifying x = 2.968912756Subproblem 2
x + 0.03125 = -3.000162756 Simplifying x + 0.03125 = -3.000162756 Reorder the terms: 0.03125 + x = -3.000162756 Solving 0.03125 + x = -3.000162756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -3.000162756 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -3.000162756 + -0.03125 x = -3.000162756 + -0.03125 Combine like terms: -3.000162756 + -0.03125 = -3.031412756 x = -3.031412756 Simplifying x = -3.031412756Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.968912756, -3.031412756}
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