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Simplifying -16x2 + 48x + 129 = 0 Reorder the terms: 129 + 48x + -16x2 = 0 Solving 129 + 48x + -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'. -8.0625 + -3x + x2 = 0 Move the constant term to the right: Add '8.0625' to each side of the equation. -8.0625 + -3x + 8.0625 + x2 = 0 + 8.0625 Reorder the terms: -8.0625 + 8.0625 + -3x + x2 = 0 + 8.0625 Combine like terms: -8.0625 + 8.0625 = 0.0000 0.0000 + -3x + x2 = 0 + 8.0625 -3x + x2 = 0 + 8.0625 Combine like terms: 0 + 8.0625 = 8.0625 -3x + x2 = 8.0625 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 8.0625 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 8.0625 + 2.25 Combine like terms: 8.0625 + 2.25 = 10.3125 2.25 + -3x + x2 = 10.3125 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.3125 Calculate the square root of the right side: 3.211308145 Break this problem into two subproblems by setting (x + -1.5) equal to 3.211308145 and -3.211308145.Subproblem 1
x + -1.5 = 3.211308145 Simplifying x + -1.5 = 3.211308145 Reorder the terms: -1.5 + x = 3.211308145 Solving -1.5 + x = 3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.211308145 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.211308145 + 1.5 x = 3.211308145 + 1.5 Combine like terms: 3.211308145 + 1.5 = 4.711308145 x = 4.711308145 Simplifying x = 4.711308145Subproblem 2
x + -1.5 = -3.211308145 Simplifying x + -1.5 = -3.211308145 Reorder the terms: -1.5 + x = -3.211308145 Solving -1.5 + x = -3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.211308145 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.211308145 + 1.5 x = -3.211308145 + 1.5 Combine like terms: -3.211308145 + 1.5 = -1.711308145 x = -1.711308145 Simplifying x = -1.711308145Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.711308145, -1.711308145}
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