x^3+4x^2+13x=0

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Solution for x^3+4x^2+13x=0 equation:


Simplifying
x3 + 4x2 + 13x = 0

Reorder the terms:
13x + 4x2 + x3 = 0

Solving
13x + 4x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + 4x + x2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(13 + 4x + x2)' equal to zero and attempt to solve: Simplifying 13 + 4x + x2 = 0 Solving 13 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 4x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 4x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 4x + x2 = 0 + -13 4x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 4x + x2 = -13 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 = -13 + 4 Reorder the terms: 4 + 4x + x2 = -13 + 4 Combine like terms: -13 + 4 = -9 4 + 4x + x2 = -9 Factor a perfect square on the left side: (x + 2)(x + 2) = -9 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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