4x^3-120x^2+625x=0

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Solution for 4x^3-120x^2+625x=0 equation:


Simplifying
4x3 + -120x2 + 625x = 0

Reorder the terms:
625x + -120x2 + 4x3 = 0

Solving
625x + -120x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(625 + -120x + 4x2) = 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 '(625 + -120x + 4x2)' equal to zero and attempt to solve: Simplifying 625 + -120x + 4x2 = 0 Solving 625 + -120x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 156.25 + -30x + x2 = 0 Move the constant term to the right: Add '-156.25' to each side of the equation. 156.25 + -30x + -156.25 + x2 = 0 + -156.25 Reorder the terms: 156.25 + -156.25 + -30x + x2 = 0 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + -30x + x2 = 0 + -156.25 -30x + x2 = 0 + -156.25 Combine like terms: 0 + -156.25 = -156.25 -30x + x2 = -156.25 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -156.25 + 225 Reorder the terms: 225 + -30x + x2 = -156.25 + 225 Combine like terms: -156.25 + 225 = 68.75 225 + -30x + x2 = 68.75 Factor a perfect square on the left side: (x + -15)(x + -15) = 68.75 Calculate the square root of the right side: 8.291561976 Break this problem into two subproblems by setting (x + -15) equal to 8.291561976 and -8.291561976.

Subproblem 1

x + -15 = 8.291561976 Simplifying x + -15 = 8.291561976 Reorder the terms: -15 + x = 8.291561976 Solving -15 + x = 8.291561976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 8.291561976 + 15 Combine like terms: -15 + 15 = 0 0 + x = 8.291561976 + 15 x = 8.291561976 + 15 Combine like terms: 8.291561976 + 15 = 23.291561976 x = 23.291561976 Simplifying x = 23.291561976

Subproblem 2

x + -15 = -8.291561976 Simplifying x + -15 = -8.291561976 Reorder the terms: -15 + x = -8.291561976 Solving -15 + x = -8.291561976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -8.291561976 + 15 Combine like terms: -15 + 15 = 0 0 + x = -8.291561976 + 15 x = -8.291561976 + 15 Combine like terms: -8.291561976 + 15 = 6.708438024 x = 6.708438024 Simplifying x = 6.708438024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.291561976, 6.708438024}

Solution

x = {0, 23.291561976, 6.708438024}

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