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Simplifying x4 + -8x3 + -12x2 = 0 Reorder the terms: -12x2 + -8x3 + x4 = 0 Solving -12x2 + -8x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-12 + -8x + x2) = 0Subproblem 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 '(-12 + -8x + x2)' equal to zero and attempt to solve: Simplifying -12 + -8x + x2 = 0 Solving -12 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -8x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -8x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -8x + x2 = 0 + 12 -8x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -8x + x2 = 12 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 = 12 + 16 Reorder the terms: 16 + -8x + x2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + -8x + x2 = 28 Factor a perfect square on the left side: (x + -4)(x + -4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -4) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -4 = 5.291502622 Simplifying x + -4 = 5.291502622 Reorder the terms: -4 + x = 5.291502622 Solving -4 + x = 5.291502622 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 = 5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.291502622 + 4 x = 5.291502622 + 4 Combine like terms: 5.291502622 + 4 = 9.291502622 x = 9.291502622 Simplifying x = 9.291502622Subproblem 2
x + -4 = -5.291502622 Simplifying x + -4 = -5.291502622 Reorder the terms: -4 + x = -5.291502622 Solving -4 + x = -5.291502622 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 = -5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.291502622 + 4 x = -5.291502622 + 4 Combine like terms: -5.291502622 + 4 = -1.291502622 x = -1.291502622 Simplifying x = -1.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.291502622, -1.291502622}Solution
x = {0, 9.291502622, -1.291502622}
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