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Simplifying 4x4 + 12x3 + 24x2 = 0 Reorder the terms: 24x2 + 12x3 + 4x4 = 0 Solving 24x2 + 12x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(6 + 3x + x2) = 0 Ignore the factor 4.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 '(6 + 3x + x2)' equal to zero and attempt to solve: Simplifying 6 + 3x + x2 = 0 Solving 6 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 3x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 3x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3x + x2 = 0 + -6 3x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 3x + x2 = -6 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + 3x + x2 = -3.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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