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Simplifying X2 + 16X = 48 Reorder the terms: 16X + X2 = 48 Solving 16X + X2 = 48 Solving for variable 'X'. Reorder the terms: -48 + 16X + X2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 16X + X2 = 0 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 = 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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