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Simplifying x2 + 16x = 126 Reorder the terms: 16x + x2 = 126 Solving 16x + x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 16x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + 16x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 16x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 16x + x2 = 0 + 126 16x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 16x + x2 = 126 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 = 126 + 64 Reorder the terms: 64 + 16x + x2 = 126 + 64 Combine like terms: 126 + 64 = 190 64 + 16x + x2 = 190 Factor a perfect square on the left side: (x + 8)(x + 8) = 190 Calculate the square root of the right side: 13.784048752 Break this problem into two subproblems by setting (x + 8) equal to 13.784048752 and -13.784048752.Subproblem 1
x + 8 = 13.784048752 Simplifying x + 8 = 13.784048752 Reorder the terms: 8 + x = 13.784048752 Solving 8 + x = 13.784048752 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 = 13.784048752 + -8 Combine like terms: 8 + -8 = 0 0 + x = 13.784048752 + -8 x = 13.784048752 + -8 Combine like terms: 13.784048752 + -8 = 5.784048752 x = 5.784048752 Simplifying x = 5.784048752Subproblem 2
x + 8 = -13.784048752 Simplifying x + 8 = -13.784048752 Reorder the terms: 8 + x = -13.784048752 Solving 8 + x = -13.784048752 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 = -13.784048752 + -8 Combine like terms: 8 + -8 = 0 0 + x = -13.784048752 + -8 x = -13.784048752 + -8 Combine like terms: -13.784048752 + -8 = -21.784048752 x = -21.784048752 Simplifying x = -21.784048752Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.784048752, -21.784048752}
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