t^2-30t+180=0

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Solution for t^2-30t+180=0 equation: 


Simplifying
t2 + -30t + 180 = 0

Reorder the terms:
180 + -30t + t2 = 0

Solving
180 + -30t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + -30t + -180 + t2 = 0 + -180

Reorder the terms:
180 + -180 + -30t + t2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + -30t + t2 = 0 + -180
-30t + t2 = 0 + -180

Combine like terms: 0 + -180 = -180
-30t + t2 = -180

The t term is -30t.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30t + 225 + t2 = -180 + 225

Reorder the terms:
225 + -30t + t2 = -180 + 225

Combine like terms: -180 + 225 = 45
225 + -30t + t2 = 45

Factor a perfect square on the left side:
(t + -15)(t + -15) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(t + -15) equal to 6.708203933 and -6.708203933.


Subproblem 1
t + -15 = 6.708203933

Simplifying
t + -15 = 6.708203933

Reorder the terms:
-15 + t = 6.708203933

Solving
-15 + t = 6.708203933

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + t = 6.708203933 + 15

Combine like terms: -15 + 15 = 0
0 + t = 6.708203933 + 15
t = 6.708203933 + 15

Combine like terms: 6.708203933 + 15 = 21.708203933
t = 21.708203933

Simplifying
t = 21.708203933


Subproblem 2
t + -15 = -6.708203933

Simplifying
t + -15 = -6.708203933

Reorder the terms:
-15 + t = -6.708203933

Solving
-15 + t = -6.708203933

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + t = -6.708203933 + 15

Combine like terms: -15 + 15 = 0
0 + t = -6.708203933 + 15
t = -6.708203933 + 15

Combine like terms: -6.708203933 + 15 = 8.291796067
t = 8.291796067

Simplifying
t = 8.291796067


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {21.708203933, 8.291796067}

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