r^4-4r^3+5r^2=0

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Solution for r^4-4r^3+5r^2=0 equation:


Simplifying
r4 + -4r3 + 5r2 = 0

Reorder the terms:
5r2 + -4r3 + r4 = 0

Solving
5r2 + -4r3 + r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(5 + -4r + r2) = 0

Subproblem 1

Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}

Subproblem 2

Set the factor '(5 + -4r + r2)' equal to zero and attempt to solve: Simplifying 5 + -4r + r2 = 0 Solving 5 + -4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4r + -5 + r2 = 0 + -5 Reorder the terms: 5 + -5 + -4r + r2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r + r2 = 0 + -5 -4r + r2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4r + r2 = -5 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = -5 + 4 Reorder the terms: 4 + -4r + r2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4r + r2 = -1 Factor a perfect square on the left side: (r + -2)(r + -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

r = {0}

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