2t^2=18t+2

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


Simplifying
2t2 = 18t + 2

Reorder the terms:
2t2 = 2 + 18t

Solving
2t2 = 2 + 18t

Solving for variable 't'.

Reorder the terms:
-2 + -18t + 2t2 = 2 + 18t + -2 + -18t

Reorder the terms:
-2 + -18t + 2t2 = 2 + -2 + 18t + -18t

Combine like terms: 2 + -2 = 0
-2 + -18t + 2t2 = 0 + 18t + -18t
-2 + -18t + 2t2 = 18t + -18t

Combine like terms: 18t + -18t = 0
-2 + -18t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -9t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -9t + t2)' equal to zero and attempt to solve:

Simplifying
-1 + -9t + t2 = 0

Solving
-1 + -9t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -9t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -9t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9t + t2 = 0 + 1
-9t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-9t + t2 = 1

The t term is -9t.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9t + 20.25 + t2 = 1 + 20.25

Reorder the terms:
20.25 + -9t + t2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + -9t + t2 = 21.25

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(t + -4.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
t + -4.5 = 4.609772229

Simplifying
t + -4.5 = 4.609772229

Reorder the terms:
-4.5 + t = 4.609772229

Solving
-4.5 + t = 4.609772229

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = 4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 4.609772229 + 4.5
t = 4.609772229 + 4.5

Combine like terms: 4.609772229 + 4.5 = 9.109772229
t = 9.109772229

Simplifying
t = 9.109772229


Subproblem 2
t + -4.5 = -4.609772229

Simplifying
t + -4.5 = -4.609772229

Reorder the terms:
-4.5 + t = -4.609772229

Solving
-4.5 + t = -4.609772229

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = -4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -4.609772229 + 4.5
t = -4.609772229 + 4.5

Combine like terms: -4.609772229 + 4.5 = -0.109772229
t = -0.109772229

Simplifying
t = -0.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.109772229, -0.109772229}
Solution
t = {9.109772229, -0.109772229}

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