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Simplifying 2X4 + -12X3 + -16X2 = 0 Reorder the terms: -16X2 + -12X3 + 2X4 = 0 Solving -16X2 + -12X3 + 2X4 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2X2'. 2X2(-8 + -6X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve: Simplifying X2 = 0 Solving X2 = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X2 = 0 Take the square root of each side: X = {0}Subproblem 2
Set the factor '(-8 + -6X + X2)' equal to zero and attempt to solve: Simplifying -8 + -6X + X2 = 0 Solving -8 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6X + 8 + X2 = 0 + 8 Reorder the terms: -8 + 8 + -6X + X2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6X + X2 = 0 + 8 -6X + X2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6X + X2 = 8 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 8 + 9 Reorder the terms: 9 + -6X + X2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6X + X2 = 17 Factor a perfect square on the left side: (X + -3)(X + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (X + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
X + -3 = 4.123105626 Simplifying X + -3 = 4.123105626 Reorder the terms: -3 + X = 4.123105626 Solving -3 + X = 4.123105626 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + X = 4.123105626 + 3 X = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 X = 7.123105626 Simplifying X = 7.123105626Subproblem 2
X + -3 = -4.123105626 Simplifying X + -3 = -4.123105626 Reorder the terms: -3 + X = -4.123105626 Solving -3 + X = -4.123105626 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + X = -4.123105626 + 3 X = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 X = -1.123105626 Simplifying X = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.123105626, -1.123105626}Solution
X = {0, 7.123105626, -1.123105626}
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