x^3+25x^2+x=0

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Solution for x^3+25x^2+x=0 equation:


Simplifying
x3 + 25x2 + x = 0

Reorder the terms:
x + 25x2 + x3 = 0

Solving
x + 25x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 25x + 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 '(1 + 25x + x2)' equal to zero and attempt to solve: Simplifying 1 + 25x + x2 = 0 Solving 1 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 25x + x2 = 0 + -1 25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 25x + x2 = -1 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -1 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -1 + 156.25 Combine like terms: -1 + 156.25 = 155.25 156.25 + 25x + x2 = 155.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (x + 12.5) equal to 12.459935794 and -12.459935794.

Subproblem 1

x + 12.5 = 12.459935794 Simplifying x + 12.5 = 12.459935794 Reorder the terms: 12.5 + x = 12.459935794 Solving 12.5 + x = 12.459935794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.459935794 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.459935794 + -12.5 x = 12.459935794 + -12.5 Combine like terms: 12.459935794 + -12.5 = -0.040064206 x = -0.040064206 Simplifying x = -0.040064206

Subproblem 2

x + 12.5 = -12.459935794 Simplifying x + 12.5 = -12.459935794 Reorder the terms: 12.5 + x = -12.459935794 Solving 12.5 + x = -12.459935794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.459935794 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.459935794 + -12.5 x = -12.459935794 + -12.5 Combine like terms: -12.459935794 + -12.5 = -24.959935794 x = -24.959935794 Simplifying x = -24.959935794

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.040064206, -24.959935794}

Solution

x = {0, -0.040064206, -24.959935794}

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