5x^4+15x^3+20x^2=

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Solution for 5x^4+15x^3+20x^2= equation:


Simplifying
5x4 + 15x3 + 20x2 = 0

Reorder the terms:
20x2 + 15x3 + 5x4 = 0

Solving
20x2 + 15x3 + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(4 + 3x + x2) = 0

Ignore the factor 5.

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 '(4 + 3x + x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + x2 = 0 Solving 4 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x + x2 = 0 + -4 3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 3x + x2 = -4 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 = -4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + 3x + x2 = -1.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -1.75 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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