t=-16t^2+220t+44

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Solution for t=-16t^2+220t+44 equation:


Simplifying
t = -16t2 + 220t + 44

Reorder the terms:
t = 44 + 220t + -16t2

Solving
t = 44 + 220t + -16t2

Solving for variable 't'.

Reorder the terms:
-44 + t + -220t + 16t2 = 44 + 220t + -16t2 + -44 + -220t + 16t2

Combine like terms: t + -220t = -219t
-44 + -219t + 16t2 = 44 + 220t + -16t2 + -44 + -220t + 16t2

Reorder the terms:
-44 + -219t + 16t2 = 44 + -44 + 220t + -220t + -16t2 + 16t2

Combine like terms: 44 + -44 = 0
-44 + -219t + 16t2 = 0 + 220t + -220t + -16t2 + 16t2
-44 + -219t + 16t2 = 220t + -220t + -16t2 + 16t2

Combine like terms: 220t + -220t = 0
-44 + -219t + 16t2 = 0 + -16t2 + 16t2
-44 + -219t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-44 + -219t + 16t2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
-2.75 + -13.6875t + t2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -13.6875t + 2.75 + t2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -13.6875t + t2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -13.6875t + t2 = 0 + 2.75
-13.6875t + t2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-13.6875t + t2 = 2.75

The t term is -13.6875t.  Take half its coefficient (-6.84375).
Square it (46.83691406) and add it to both sides.

Add '46.83691406' to each side of the equation.
-13.6875t + 46.83691406 + t2 = 2.75 + 46.83691406

Reorder the terms:
46.83691406 + -13.6875t + t2 = 2.75 + 46.83691406

Combine like terms: 2.75 + 46.83691406 = 49.58691406
46.83691406 + -13.6875t + t2 = 49.58691406

Factor a perfect square on the left side:
(t + -6.84375)(t + -6.84375) = 49.58691406

Calculate the square root of the right side: 7.041797644

Break this problem into two subproblems by setting 
(t + -6.84375) equal to 7.041797644 and -7.041797644.

Subproblem 1

t + -6.84375 = 7.041797644 Simplifying t + -6.84375 = 7.041797644 Reorder the terms: -6.84375 + t = 7.041797644 Solving -6.84375 + t = 7.041797644 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.84375' to each side of the equation. -6.84375 + 6.84375 + t = 7.041797644 + 6.84375 Combine like terms: -6.84375 + 6.84375 = 0.00000 0.00000 + t = 7.041797644 + 6.84375 t = 7.041797644 + 6.84375 Combine like terms: 7.041797644 + 6.84375 = 13.885547644 t = 13.885547644 Simplifying t = 13.885547644

Subproblem 2

t + -6.84375 = -7.041797644 Simplifying t + -6.84375 = -7.041797644 Reorder the terms: -6.84375 + t = -7.041797644 Solving -6.84375 + t = -7.041797644 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.84375' to each side of the equation. -6.84375 + 6.84375 + t = -7.041797644 + 6.84375 Combine like terms: -6.84375 + 6.84375 = 0.00000 0.00000 + t = -7.041797644 + 6.84375 t = -7.041797644 + 6.84375 Combine like terms: -7.041797644 + 6.84375 = -0.198047644 t = -0.198047644 Simplifying t = -0.198047644

Solution

The solution to the problem is based on the solutions from the subproblems. t = {13.885547644, -0.198047644}

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