2t^2-36t+6=0

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Solution for 2t^2-36t+6=0 equation:


Simplifying
2t2 + -36t + 6 = 0

Reorder the terms:
6 + -36t + 2t2 = 0

Solving
6 + -36t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -18t + t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -18t + t2)' equal to zero and attempt to solve: Simplifying 3 + -18t + t2 = 0 Solving 3 + -18t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -18t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -18t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -18t + t2 = 0 + -3 -18t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -18t + t2 = -3 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 = -3 + 81 Reorder the terms: 81 + -18t + t2 = -3 + 81 Combine like terms: -3 + 81 = 78 81 + -18t + t2 = 78 Factor a perfect square on the left side: (t + -9)(t + -9) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (t + -9) equal to 8.831760866 and -8.831760866.

Subproblem 1

t + -9 = 8.831760866 Simplifying t + -9 = 8.831760866 Reorder the terms: -9 + t = 8.831760866 Solving -9 + t = 8.831760866 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 = 8.831760866 + 9 Combine like terms: -9 + 9 = 0 0 + t = 8.831760866 + 9 t = 8.831760866 + 9 Combine like terms: 8.831760866 + 9 = 17.831760866 t = 17.831760866 Simplifying t = 17.831760866

Subproblem 2

t + -9 = -8.831760866 Simplifying t + -9 = -8.831760866 Reorder the terms: -9 + t = -8.831760866 Solving -9 + t = -8.831760866 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 = -8.831760866 + 9 Combine like terms: -9 + 9 = 0 0 + t = -8.831760866 + 9 t = -8.831760866 + 9 Combine like terms: -8.831760866 + 9 = 0.168239134 t = 0.168239134 Simplifying t = 0.168239134

Solution

The solution to the problem is based on the solutions from the subproblems. t = {17.831760866, 0.168239134}

Solution

t = {17.831760866, 0.168239134}

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