x^3+48x^2+80x=0

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Solution for x^3+48x^2+80x=0 equation:


Simplifying
x3 + 48x2 + 80x = 0

Reorder the terms:
80x + 48x2 + x3 = 0

Solving
80x + 48x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(80 + 48x + 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 '(80 + 48x + x2)' equal to zero and attempt to solve: Simplifying 80 + 48x + x2 = 0 Solving 80 + 48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 48x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 48x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 48x + x2 = 0 + -80 48x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 48x + x2 = -80 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = -80 + 576 Reorder the terms: 576 + 48x + x2 = -80 + 576 Combine like terms: -80 + 576 = 496 576 + 48x + x2 = 496 Factor a perfect square on the left side: (x + 24)(x + 24) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + 24) equal to 22.271057451 and -22.271057451.

Subproblem 1

x + 24 = 22.271057451 Simplifying x + 24 = 22.271057451 Reorder the terms: 24 + x = 22.271057451 Solving 24 + x = 22.271057451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 22.271057451 + -24 Combine like terms: 24 + -24 = 0 0 + x = 22.271057451 + -24 x = 22.271057451 + -24 Combine like terms: 22.271057451 + -24 = -1.728942549 x = -1.728942549 Simplifying x = -1.728942549

Subproblem 2

x + 24 = -22.271057451 Simplifying x + 24 = -22.271057451 Reorder the terms: 24 + x = -22.271057451 Solving 24 + x = -22.271057451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -22.271057451 + -24 Combine like terms: 24 + -24 = 0 0 + x = -22.271057451 + -24 x = -22.271057451 + -24 Combine like terms: -22.271057451 + -24 = -46.271057451 x = -46.271057451 Simplifying x = -46.271057451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.728942549, -46.271057451}

Solution

x = {0, -1.728942549, -46.271057451}

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