-16t^2+224t+10=0

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Solution for -16t^2+224t+10=0 equation: 


Simplifying
-16t2 + 224t + 10 = 0

Reorder the terms:
10 + 224t + -16t2 = 0

Solving
10 + 224t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 112t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 112t + -8t2)' equal to zero and attempt to solve:

Simplifying
5 + 112t + -8t2 = 0

Solving
5 + 112t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.625 + -14t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -14t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -14t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -14t + t2 = 0 + 0.625
-14t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-14t + t2 = 0.625

The t term is -14t.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14t + 49 + t2 = 0.625 + 49

Reorder the terms:
49 + -14t + t2 = 0.625 + 49

Combine like terms: 0.625 + 49 = 49.625
49 + -14t + t2 = 49.625

Factor a perfect square on the left side:
(t + -7)(t + -7) = 49.625

Calculate the square root of the right side: 7.044501402

Break this problem into two subproblems by setting 
(t + -7) equal to 7.044501402 and -7.044501402.


Subproblem 1
t + -7 = 7.044501402

Simplifying
t + -7 = 7.044501402

Reorder the terms:
-7 + t = 7.044501402

Solving
-7 + t = 7.044501402

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = 7.044501402 + 7

Combine like terms: -7 + 7 = 0
0 + t = 7.044501402 + 7
t = 7.044501402 + 7

Combine like terms: 7.044501402 + 7 = 14.044501402
t = 14.044501402

Simplifying
t = 14.044501402


Subproblem 2
t + -7 = -7.044501402

Simplifying
t + -7 = -7.044501402

Reorder the terms:
-7 + t = -7.044501402

Solving
-7 + t = -7.044501402

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = -7.044501402 + 7

Combine like terms: -7 + 7 = 0
0 + t = -7.044501402 + 7
t = -7.044501402 + 7

Combine like terms: -7.044501402 + 7 = -0.044501402
t = -0.044501402

Simplifying
t = -0.044501402


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.044501402, -0.044501402}
Solution
t = {14.044501402, -0.044501402}

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