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Simplifying x4 + -16x3 + 4x2 = 0 Reorder the terms: 4x2 + -16x3 + x4 = 0 Solving 4x2 + -16x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(4 + -16x + 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 '(4 + -16x + x2)' equal to zero and attempt to solve: Simplifying 4 + -16x + x2 = 0 Solving 4 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -16x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -16x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -16x + x2 = 0 + -4 -16x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -16x + x2 = -4 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -4 + 64 Reorder the terms: 64 + -16x + x2 = -4 + 64 Combine like terms: -4 + 64 = 60 64 + -16x + x2 = 60 Factor a perfect square on the left side: (x + -8)(x + -8) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -8) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -8 = 7.745966692 Simplifying x + -8 = 7.745966692 Reorder the terms: -8 + x = 7.745966692 Solving -8 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.745966692 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.745966692 + 8 x = 7.745966692 + 8 Combine like terms: 7.745966692 + 8 = 15.745966692 x = 15.745966692 Simplifying x = 15.745966692Subproblem 2
x + -8 = -7.745966692 Simplifying x + -8 = -7.745966692 Reorder the terms: -8 + x = -7.745966692 Solving -8 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.745966692 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.745966692 + 8 x = -7.745966692 + 8 Combine like terms: -7.745966692 + 8 = 0.254033308 x = 0.254033308 Simplifying x = 0.254033308Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.745966692, 0.254033308}Solution
x = {0, 15.745966692, 0.254033308}
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