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Simplifying 3X2 + 24X + 16 = 169 Reorder the terms: 16 + 24X + 3X2 = 169 Solving 16 + 24X + 3X2 = 169 Solving for variable 'X'. Reorder the terms: 16 + -169 + 24X + 3X2 = 169 + -169 Combine like terms: 16 + -169 = -153 -153 + 24X + 3X2 = 169 + -169 Combine like terms: 169 + -169 = 0 -153 + 24X + 3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-51 + 8X + X2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-51 + 8X + X2)' equal to zero and attempt to solve: Simplifying -51 + 8X + X2 = 0 Solving -51 + 8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 8X + 51 + X2 = 0 + 51 Reorder the terms: -51 + 51 + 8X + X2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 8X + X2 = 0 + 51 8X + X2 = 0 + 51 Combine like terms: 0 + 51 = 51 8X + X2 = 51 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 = 51 + 16 Reorder the terms: 16 + 8X + X2 = 51 + 16 Combine like terms: 51 + 16 = 67 16 + 8X + X2 = 67 Factor a perfect square on the left side: (X + 4)(X + 4) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (X + 4) equal to 8.185352772 and -8.185352772.Subproblem 1
X + 4 = 8.185352772 Simplifying X + 4 = 8.185352772 Reorder the terms: 4 + X = 8.185352772 Solving 4 + X = 8.185352772 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 = 8.185352772 + -4 Combine like terms: 4 + -4 = 0 0 + X = 8.185352772 + -4 X = 8.185352772 + -4 Combine like terms: 8.185352772 + -4 = 4.185352772 X = 4.185352772 Simplifying X = 4.185352772Subproblem 2
X + 4 = -8.185352772 Simplifying X + 4 = -8.185352772 Reorder the terms: 4 + X = -8.185352772 Solving 4 + X = -8.185352772 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 = -8.185352772 + -4 Combine like terms: 4 + -4 = 0 0 + X = -8.185352772 + -4 X = -8.185352772 + -4 Combine like terms: -8.185352772 + -4 = -12.185352772 X = -12.185352772 Simplifying X = -12.185352772Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.185352772, -12.185352772}Solution
X = {4.185352772, -12.185352772}
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