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Simplifying 0 = x2 + 16x + -48 Reorder the terms: 0 = -48 + 16x + x2 Solving 0 = -48 + 16x + x2 Solving for variable 'x'. Combine like terms: 0 + 48 = 48 48 + -16x + -1x2 = -48 + 16x + x2 + 48 + -16x + -1x2 Reorder the terms: 48 + -16x + -1x2 = -48 + 48 + 16x + -16x + x2 + -1x2 Combine like terms: -48 + 48 = 0 48 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 48 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 48 + -16x + -1x2 = 0 + x2 + -1x2 48 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 48 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 16x + x2 = 0 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 = 2.583005244 x = 2.583005244 Simplifying x = 2.583005244Subproblem 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 = -18.583005244 x = -18.583005244 Simplifying x = -18.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.583005244, -18.583005244}
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