154-10t-16t^2=0

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Solution for 154-10t-16t^2=0 equation: 


Simplifying
154 + -10t + -16t2 = 0

Solving
154 + -10t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(77 + -5t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(77 + -5t + -8t2)' equal to zero and attempt to solve:

Simplifying
77 + -5t + -8t2 = 0

Solving
77 + -5t + -8t2 = 0

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

Divide each side by '-8'.
-9.625 + 0.625t + t2 = 0

Move the constant term to the right:

Add '9.625' to each side of the equation.
-9.625 + 0.625t + 9.625 + t2 = 0 + 9.625

Reorder the terms:
-9.625 + 9.625 + 0.625t + t2 = 0 + 9.625

Combine like terms: -9.625 + 9.625 = 0.000
0.000 + 0.625t + t2 = 0 + 9.625
0.625t + t2 = 0 + 9.625

Combine like terms: 0 + 9.625 = 9.625
0.625t + t2 = 9.625

The t term is 0.625t.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625t + 0.09765625 + t2 = 9.625 + 0.09765625

Reorder the terms:
0.09765625 + 0.625t + t2 = 9.625 + 0.09765625

Combine like terms: 9.625 + 0.09765625 = 9.72265625
0.09765625 + 0.625t + t2 = 9.72265625

Factor a perfect square on the left side:
(t + 0.3125)(t + 0.3125) = 9.72265625

Calculate the square root of the right side: 3.118117421

Break this problem into two subproblems by setting 
(t + 0.3125) equal to 3.118117421 and -3.118117421.


Subproblem 1
t + 0.3125 = 3.118117421

Simplifying
t + 0.3125 = 3.118117421

Reorder the terms:
0.3125 + t = 3.118117421

Solving
0.3125 + t = 3.118117421

Solving for variable 't'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + t = 3.118117421 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = 3.118117421 + -0.3125
t = 3.118117421 + -0.3125

Combine like terms: 3.118117421 + -0.3125 = 2.805617421
t = 2.805617421

Simplifying
t = 2.805617421


Subproblem 2
t + 0.3125 = -3.118117421

Simplifying
t + 0.3125 = -3.118117421

Reorder the terms:
0.3125 + t = -3.118117421

Solving
0.3125 + t = -3.118117421

Solving for variable 't'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + t = -3.118117421 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = -3.118117421 + -0.3125
t = -3.118117421 + -0.3125

Combine like terms: -3.118117421 + -0.3125 = -3.430617421
t = -3.430617421

Simplifying
t = -3.430617421


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.805617421, -3.430617421}
Solution
t = {2.805617421, -3.430617421}

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