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Simplifying 2X2 = 16X + 8 Reorder the terms: 2X2 = 8 + 16X Solving 2X2 = 8 + 16X Solving for variable 'X'. Reorder the terms: -8 + -16X + 2X2 = 8 + 16X + -8 + -16X Reorder the terms: -8 + -16X + 2X2 = 8 + -8 + 16X + -16X Combine like terms: 8 + -8 = 0 -8 + -16X + 2X2 = 0 + 16X + -16X -8 + -16X + 2X2 = 16X + -16X Combine like terms: 16X + -16X = 0 -8 + -16X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -8X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -8X + X2)' equal to zero and attempt to solve: Simplifying -4 + -8X + X2 = 0 Solving -4 + -8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -8X + 4 + X2 = 0 + 4 Reorder the terms: -4 + 4 + -8X + X2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8X + X2 = 0 + 4 -8X + X2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8X + X2 = 4 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 = 4 + 16 Reorder the terms: 16 + -8X + X2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8X + X2 = 20 Factor a perfect square on the left side: (X + -4)(X + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (X + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
X + -4 = 4.472135955 Simplifying X + -4 = 4.472135955 Reorder the terms: -4 + X = 4.472135955 Solving -4 + X = 4.472135955 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 = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + X = 4.472135955 + 4 X = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 X = 8.472135955 Simplifying X = 8.472135955Subproblem 2
X + -4 = -4.472135955 Simplifying X + -4 = -4.472135955 Reorder the terms: -4 + X = -4.472135955 Solving -4 + X = -4.472135955 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 = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + X = -4.472135955 + 4 X = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 X = -0.472135955 Simplifying X = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.472135955, -0.472135955}Solution
X = {8.472135955, -0.472135955}
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