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Simplifying x2 + -16x + -48 = 0 Reorder the terms: -48 + -16x + x2 = 0 Solving -48 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -16x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -16x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -16x + x2 = 0 + 48 -16x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -16x + x2 = 48 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 = 48 + 64 Reorder the terms: 64 + -16x + x2 = 48 + 64 Combine like terms: 48 + 64 = 112 64 + -16x + x2 = 112 Factor a perfect square on the left side: (x + -8)(x + -8) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + -8) equal to 10.583005244 and -10.583005244.Subproblem 1
x + -8 = 10.583005244 Simplifying x + -8 = 10.583005244 Reorder the terms: -8 + x = 10.583005244 Solving -8 + x = 10.583005244 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 = 10.583005244 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.583005244 + 8 x = 10.583005244 + 8 Combine like terms: 10.583005244 + 8 = 18.583005244 x = 18.583005244 Simplifying x = 18.583005244Subproblem 2
x + -8 = -10.583005244 Simplifying x + -8 = -10.583005244 Reorder the terms: -8 + x = -10.583005244 Solving -8 + x = -10.583005244 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 = -10.583005244 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.583005244 + 8 x = -10.583005244 + 8 Combine like terms: -10.583005244 + 8 = -2.583005244 x = -2.583005244 Simplifying x = -2.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.583005244, -2.583005244}
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