t^2-30t+20=0

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Solution for t^2-30t+20=0 equation: 


Simplifying
t2 + -30t + 20 = 0

Reorder the terms:
20 + -30t + t2 = 0

Solving
20 + -30t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -30t + -20 + t2 = 0 + -20

Reorder the terms:
20 + -20 + -30t + t2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -30t + t2 = 0 + -20
-30t + t2 = 0 + -20

Combine like terms: 0 + -20 = -20
-30t + t2 = -20

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 = -20 + 225

Reorder the terms:
225 + -30t + t2 = -20 + 225

Combine like terms: -20 + 225 = 205
225 + -30t + t2 = 205

Factor a perfect square on the left side:
(t + -15)(t + -15) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(t + -15) equal to 14.317821063 and -14.317821063.


Subproblem 1
t + -15 = 14.317821063

Simplifying
t + -15 = 14.317821063

Reorder the terms:
-15 + t = 14.317821063

Solving
-15 + t = 14.317821063

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 = 14.317821063 + 15

Combine like terms: -15 + 15 = 0
0 + t = 14.317821063 + 15
t = 14.317821063 + 15

Combine like terms: 14.317821063 + 15 = 29.317821063
t = 29.317821063

Simplifying
t = 29.317821063


Subproblem 2
t + -15 = -14.317821063

Simplifying
t + -15 = -14.317821063

Reorder the terms:
-15 + t = -14.317821063

Solving
-15 + t = -14.317821063

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 = -14.317821063 + 15

Combine like terms: -15 + 15 = 0
0 + t = -14.317821063 + 15
t = -14.317821063 + 15

Combine like terms: -14.317821063 + 15 = 0.682178937
t = 0.682178937

Simplifying
t = 0.682178937


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {29.317821063, 0.682178937}

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