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Simplifying x4 + 12x3 + -8x2 = 0 Reorder the terms: -8x2 + 12x3 + x4 = 0 Solving -8x2 + 12x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-8 + 12x + 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 '(-8 + 12x + x2)' equal to zero and attempt to solve: Simplifying -8 + 12x + x2 = 0 Solving -8 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 12x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 12x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 12x + x2 = 0 + 8 12x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 12x + x2 = 8 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 8 + 36 Reorder the terms: 36 + 12x + x2 = 8 + 36 Combine like terms: 8 + 36 = 44 36 + 12x + x2 = 44 Factor a perfect square on the left side: (x + 6)(x + 6) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 6) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 6 = 6.633249581 Simplifying x + 6 = 6.633249581 Reorder the terms: 6 + x = 6.633249581 Solving 6 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.633249581 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.633249581 + -6 x = 6.633249581 + -6 Combine like terms: 6.633249581 + -6 = 0.633249581 x = 0.633249581 Simplifying x = 0.633249581Subproblem 2
x + 6 = -6.633249581 Simplifying x + 6 = -6.633249581 Reorder the terms: 6 + x = -6.633249581 Solving 6 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.633249581 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.633249581 + -6 x = -6.633249581 + -6 Combine like terms: -6.633249581 + -6 = -12.633249581 x = -12.633249581 Simplifying x = -12.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.633249581, -12.633249581}Solution
x = {0, 0.633249581, -12.633249581}
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