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Simplifying 2x2 + 16x = 336 Reorder the terms: 16x + 2x2 = 336 Solving 16x + 2x2 = 336 Solving for variable 'x'. Reorder the terms: -336 + 16x + 2x2 = 336 + -336 Combine like terms: 336 + -336 = 0 -336 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-168 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-168 + 8x + x2)' equal to zero and attempt to solve: Simplifying -168 + 8x + x2 = 0 Solving -168 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 8x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 8x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 8x + x2 = 0 + 168 8x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 8x + x2 = 168 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 168 + 16 Reorder the terms: 16 + 8x + x2 = 168 + 16 Combine like terms: 168 + 16 = 184 16 + 8x + x2 = 184 Factor a perfect square on the left side: (x + 4)(x + 4) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + 4) equal to 13.564659966 and -13.564659966.Subproblem 1
x + 4 = 13.564659966 Simplifying x + 4 = 13.564659966 Reorder the terms: 4 + x = 13.564659966 Solving 4 + x = 13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 13.564659966 + -4 Combine like terms: 4 + -4 = 0 0 + x = 13.564659966 + -4 x = 13.564659966 + -4 Combine like terms: 13.564659966 + -4 = 9.564659966 x = 9.564659966 Simplifying x = 9.564659966Subproblem 2
x + 4 = -13.564659966 Simplifying x + 4 = -13.564659966 Reorder the terms: 4 + x = -13.564659966 Solving 4 + x = -13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -13.564659966 + -4 Combine like terms: 4 + -4 = 0 0 + x = -13.564659966 + -4 x = -13.564659966 + -4 Combine like terms: -13.564659966 + -4 = -17.564659966 x = -17.564659966 Simplifying x = -17.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.564659966, -17.564659966}Solution
x = {9.564659966, -17.564659966}
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