22=-2t^2-4t+18t+36

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Solution for 22=-2t^2-4t+18t+36 equation: 


Simplifying
22 = -2t2 + -4t + 18t + 36

Reorder the terms:
22 = 36 + -4t + 18t + -2t2

Combine like terms: -4t + 18t = 14t
22 = 36 + 14t + -2t2

Solving
22 = 36 + 14t + -2t2

Solving for variable 't'.

Combine like terms: 22 + -36 = -14
-14 + -14t + 2t2 = 36 + 14t + -2t2 + -36 + -14t + 2t2

Reorder the terms:
-14 + -14t + 2t2 = 36 + -36 + 14t + -14t + -2t2 + 2t2

Combine like terms: 36 + -36 = 0
-14 + -14t + 2t2 = 0 + 14t + -14t + -2t2 + 2t2
-14 + -14t + 2t2 = 14t + -14t + -2t2 + 2t2

Combine like terms: 14t + -14t = 0
-14 + -14t + 2t2 = 0 + -2t2 + 2t2
-14 + -14t + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-14 + -14t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -7t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -7t + t2)' equal to zero and attempt to solve:

Simplifying
-7 + -7t + t2 = 0

Solving
-7 + -7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -7t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -7t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -7t + t2 = 0 + 7
-7t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-7t + t2 = 7

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 7 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 7 + 12.25

Combine like terms: 7 + 12.25 = 19.25
12.25 + -7t + t2 = 19.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(t + -3.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
t + -3.5 = 4.387482194

Simplifying
t + -3.5 = 4.387482194

Reorder the terms:
-3.5 + t = 4.387482194

Solving
-3.5 + t = 4.387482194

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 4.387482194 + 3.5
t = 4.387482194 + 3.5

Combine like terms: 4.387482194 + 3.5 = 7.887482194
t = 7.887482194

Simplifying
t = 7.887482194


Subproblem 2
t + -3.5 = -4.387482194

Simplifying
t + -3.5 = -4.387482194

Reorder the terms:
-3.5 + t = -4.387482194

Solving
-3.5 + t = -4.387482194

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -4.387482194 + 3.5
t = -4.387482194 + 3.5

Combine like terms: -4.387482194 + 3.5 = -0.887482194
t = -0.887482194

Simplifying
t = -0.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.887482194, -0.887482194}
Solution
t = {7.887482194, -0.887482194}

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