t^3+18t^2+18t=0

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Solution for t^3+18t^2+18t=0 equation:


Simplifying
t3 + 18t2 + 18t = 0

Reorder the terms:
18t + 18t2 + t3 = 0

Solving
18t + 18t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(18 + 18t + 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 '(18 + 18t + t2)' equal to zero and attempt to solve: Simplifying 18 + 18t + t2 = 0 Solving 18 + 18t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 18t + -18 + t2 = 0 + -18 Reorder the terms: 18 + -18 + 18t + t2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 18t + t2 = 0 + -18 18t + t2 = 0 + -18 Combine like terms: 0 + -18 = -18 18t + t2 = -18 The t term is 18t. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18t + 81 + t2 = -18 + 81 Reorder the terms: 81 + 18t + t2 = -18 + 81 Combine like terms: -18 + 81 = 63 81 + 18t + t2 = 63 Factor a perfect square on the left side: (t + 9)(t + 9) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (t + 9) equal to 7.937253933 and -7.937253933.

Subproblem 1

t + 9 = 7.937253933 Simplifying t + 9 = 7.937253933 Reorder the terms: 9 + t = 7.937253933 Solving 9 + t = 7.937253933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = 7.937253933 + -9 Combine like terms: 9 + -9 = 0 0 + t = 7.937253933 + -9 t = 7.937253933 + -9 Combine like terms: 7.937253933 + -9 = -1.062746067 t = -1.062746067 Simplifying t = -1.062746067

Subproblem 2

t + 9 = -7.937253933 Simplifying t + 9 = -7.937253933 Reorder the terms: 9 + t = -7.937253933 Solving 9 + t = -7.937253933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = -7.937253933 + -9 Combine like terms: 9 + -9 = 0 0 + t = -7.937253933 + -9 t = -7.937253933 + -9 Combine like terms: -7.937253933 + -9 = -16.937253933 t = -16.937253933 Simplifying t = -16.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-1.062746067, -16.937253933}

Solution

t = {0, -1.062746067, -16.937253933}

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