-16t^2+100t-90=0

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Solution for -16t^2+100t-90=0 equation: 


Simplifying
-16t2 + 100t + -90 = 0

Reorder the terms:
-90 + 100t + -16t2 = 0

Solving
-90 + 100t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 50t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 50t + -8t2)' equal to zero and attempt to solve:

Simplifying
-45 + 50t + -8t2 = 0

Solving
-45 + 50t + -8t2 = 0

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

Divide each side by '-8'.
5.625 + -6.25t + t2 = 0

Move the constant term to the right:

Add '-5.625' to each side of the equation.
5.625 + -6.25t + -5.625 + t2 = 0 + -5.625

Reorder the terms:
5.625 + -5.625 + -6.25t + t2 = 0 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + -6.25t + t2 = 0 + -5.625
-6.25t + t2 = 0 + -5.625

Combine like terms: 0 + -5.625 = -5.625
-6.25t + t2 = -5.625

The t term is -6.25t.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25t + 9.765625 + t2 = -5.625 + 9.765625

Reorder the terms:
9.765625 + -6.25t + t2 = -5.625 + 9.765625

Combine like terms: -5.625 + 9.765625 = 4.140625
9.765625 + -6.25t + t2 = 4.140625

Factor a perfect square on the left side:
(t + -3.125)(t + -3.125) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(t + -3.125) equal to 2.034852575 and -2.034852575.


Subproblem 1
t + -3.125 = 2.034852575

Simplifying
t + -3.125 = 2.034852575

Reorder the terms:
-3.125 + t = 2.034852575

Solving
-3.125 + t = 2.034852575

Solving for variable 't'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + t = 2.034852575 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = 2.034852575 + 3.125
t = 2.034852575 + 3.125

Combine like terms: 2.034852575 + 3.125 = 5.159852575
t = 5.159852575

Simplifying
t = 5.159852575


Subproblem 2
t + -3.125 = -2.034852575

Simplifying
t + -3.125 = -2.034852575

Reorder the terms:
-3.125 + t = -2.034852575

Solving
-3.125 + t = -2.034852575

Solving for variable 't'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + t = -2.034852575 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = -2.034852575 + 3.125
t = -2.034852575 + 3.125

Combine like terms: -2.034852575 + 3.125 = 1.090147425
t = 1.090147425

Simplifying
t = 1.090147425


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.159852575, 1.090147425}
Solution
t = {5.159852575, 1.090147425}

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