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Simplifying x4 + 4x3 + 5x2 = 0 Reorder the terms: 5x2 + 4x3 + x4 = 0 Solving 5x2 + 4x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(5 + 4x + 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 '(5 + 4x + x2)' equal to zero and attempt to solve: Simplifying 5 + 4x + x2 = 0 Solving 5 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 4x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x + x2 = 0 + -5 4x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 4x + x2 = -5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -5 + 4 Reorder the terms: 4 + 4x + x2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4x + x2 = -1 Factor a perfect square on the left side: (x + 2)(x + 2) = -1 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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