t^2-36t+108=0

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Solution for t^2-36t+108=0 equation:


Simplifying
t2 + -36t + 108 = 0

Reorder the terms:
108 + -36t + t2 = 0

Solving
108 + -36t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-108' to each side of the equation.
108 + -36t + -108 + t2 = 0 + -108

Reorder the terms:
108 + -108 + -36t + t2 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + -36t + t2 = 0 + -108
-36t + t2 = 0 + -108

Combine like terms: 0 + -108 = -108
-36t + t2 = -108

The t term is -36t.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36t + 324 + t2 = -108 + 324

Reorder the terms:
324 + -36t + t2 = -108 + 324

Combine like terms: -108 + 324 = 216
324 + -36t + t2 = 216

Factor a perfect square on the left side:
(t + -18)(t + -18) = 216

Calculate the square root of the right side: 14.696938457

Break this problem into two subproblems by setting 
(t + -18) equal to 14.696938457 and -14.696938457.

Subproblem 1

t + -18 = 14.696938457 Simplifying t + -18 = 14.696938457 Reorder the terms: -18 + t = 14.696938457 Solving -18 + t = 14.696938457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = 14.696938457 + 18 Combine like terms: -18 + 18 = 0 0 + t = 14.696938457 + 18 t = 14.696938457 + 18 Combine like terms: 14.696938457 + 18 = 32.696938457 t = 32.696938457 Simplifying t = 32.696938457

Subproblem 2

t + -18 = -14.696938457 Simplifying t + -18 = -14.696938457 Reorder the terms: -18 + t = -14.696938457 Solving -18 + t = -14.696938457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = -14.696938457 + 18 Combine like terms: -18 + 18 = 0 0 + t = -14.696938457 + 18 t = -14.696938457 + 18 Combine like terms: -14.696938457 + 18 = 3.303061543 t = 3.303061543 Simplifying t = 3.303061543

Solution

The solution to the problem is based on the solutions from the subproblems. t = {32.696938457, 3.303061543}

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