235(t)=-15t^2+120t+10

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Solution for 235(t)=-15t^2+120t+10 equation: 


Simplifying
235(t) = -15t2 + 120t + 10

Reorder the terms:
235t = 10 + 120t + -15t2

Solving
235t = 10 + 120t + -15t2

Solving for variable 't'.

Reorder the terms:
-10 + 235t + -120t + 15t2 = 10 + 120t + -15t2 + -10 + -120t + 15t2

Combine like terms: 235t + -120t = 115t
-10 + 115t + 15t2 = 10 + 120t + -15t2 + -10 + -120t + 15t2

Reorder the terms:
-10 + 115t + 15t2 = 10 + -10 + 120t + -120t + -15t2 + 15t2

Combine like terms: 10 + -10 = 0
-10 + 115t + 15t2 = 0 + 120t + -120t + -15t2 + 15t2
-10 + 115t + 15t2 = 120t + -120t + -15t2 + 15t2

Combine like terms: 120t + -120t = 0
-10 + 115t + 15t2 = 0 + -15t2 + 15t2
-10 + 115t + 15t2 = -15t2 + 15t2

Combine like terms: -15t2 + 15t2 = 0
-10 + 115t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 23t + 3t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + 23t + 3t2)' equal to zero and attempt to solve:

Simplifying
-2 + 23t + 3t2 = 0

Solving
-2 + 23t + 3t2 = 0

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

Divide each side by '3'.
-0.6666666667 + 7.666666667t + t2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 7.666666667t + 0.6666666667 + t2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 7.666666667t + t2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 7.666666667t + t2 = 0 + 0.6666666667
7.666666667t + t2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
7.666666667t + t2 = 0.6666666667

The t term is 7.666666667t.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667t + 14.69444445 + t2 = 0.6666666667 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667t + t2 = 0.6666666667 + 14.69444445

Combine like terms: 0.6666666667 + 14.69444445 = 15.3611111167
14.69444445 + 7.666666667t + t2 = 15.3611111167

Factor a perfect square on the left side:
(t + 3.833333334)(t + 3.833333334) = 15.3611111167

Calculate the square root of the right side: 3.919325339

Break this problem into two subproblems by setting 
(t + 3.833333334) equal to 3.919325339 and -3.919325339.


Subproblem 1
t + 3.833333334 = 3.919325339

Simplifying
t + 3.833333334 = 3.919325339

Reorder the terms:
3.833333334 + t = 3.919325339

Solving
3.833333334 + t = 3.919325339

Solving for variable 't'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + t = 3.919325339 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + t = 3.919325339 + -3.833333334
t = 3.919325339 + -3.833333334

Combine like terms: 3.919325339 + -3.833333334 = 0.085992005
t = 0.085992005

Simplifying
t = 0.085992005


Subproblem 2
t + 3.833333334 = -3.919325339

Simplifying
t + 3.833333334 = -3.919325339

Reorder the terms:
3.833333334 + t = -3.919325339

Solving
3.833333334 + t = -3.919325339

Solving for variable 't'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + t = -3.919325339 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + t = -3.919325339 + -3.833333334
t = -3.919325339 + -3.833333334

Combine like terms: -3.919325339 + -3.833333334 = -7.752658673
t = -7.752658673

Simplifying
t = -7.752658673


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.085992005, -7.752658673}
Solution
t = {0.085992005, -7.752658673}

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