t^3-5t^2+3t=0

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Solution for t^3-5t^2+3t=0 equation:


Simplifying
t3 + -5t2 + 3t = 0

Reorder the terms:
3t + -5t2 + t3 = 0

Solving
3t + -5t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(3 + -5t + t2) = 0

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(3 + -5t + t2)' equal to zero and attempt to solve: Simplifying 3 + -5t + t2 = 0 Solving 3 + -5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -5t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5t + t2 = 0 + -3 -5t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5t + t2 = -3 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -3 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5t + t2 = 3.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (t + -2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

t + -2.5 = 1.802775638 Simplifying t + -2.5 = 1.802775638 Reorder the terms: -2.5 + t = 1.802775638 Solving -2.5 + t = 1.802775638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.802775638 + 2.5 t = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 t = 4.302775638 Simplifying t = 4.302775638

Subproblem 2

t + -2.5 = -1.802775638 Simplifying t + -2.5 = -1.802775638 Reorder the terms: -2.5 + t = -1.802775638 Solving -2.5 + t = -1.802775638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.802775638 + 2.5 t = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 t = 0.697224362 Simplifying t = 0.697224362

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.302775638, 0.697224362}

Solution

t = {0, 4.302775638, 0.697224362}

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