-5t^2+100t-425=0

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Solution for -5t^2+100t-425=0 equation: 


Simplifying
-5t2 + 100t + -425 = 0

Reorder the terms:
-425 + 100t + -5t2 = 0

Solving
-425 + 100t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-85 + 20t + -1t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-85 + 20t + -1t2)' equal to zero and attempt to solve:

Simplifying
-85 + 20t + -1t2 = 0

Solving
-85 + 20t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
85 + -20t + t2 = 0

Move the constant term to the right:

Add '-85' to each side of the equation.
85 + -20t + -85 + t2 = 0 + -85

Reorder the terms:
85 + -85 + -20t + t2 = 0 + -85

Combine like terms: 85 + -85 = 0
0 + -20t + t2 = 0 + -85
-20t + t2 = 0 + -85

Combine like terms: 0 + -85 = -85
-20t + t2 = -85

The t term is -20t.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20t + 100 + t2 = -85 + 100

Reorder the terms:
100 + -20t + t2 = -85 + 100

Combine like terms: -85 + 100 = 15
100 + -20t + t2 = 15

Factor a perfect square on the left side:
(t + -10)(t + -10) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(t + -10) equal to 3.872983346 and -3.872983346.


Subproblem 1
t + -10 = 3.872983346

Simplifying
t + -10 = 3.872983346

Reorder the terms:
-10 + t = 3.872983346

Solving
-10 + t = 3.872983346

Solving for variable 't'.

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

Add '10' to each side of the equation.
-10 + 10 + t = 3.872983346 + 10

Combine like terms: -10 + 10 = 0
0 + t = 3.872983346 + 10
t = 3.872983346 + 10

Combine like terms: 3.872983346 + 10 = 13.872983346
t = 13.872983346

Simplifying
t = 13.872983346


Subproblem 2
t + -10 = -3.872983346

Simplifying
t + -10 = -3.872983346

Reorder the terms:
-10 + t = -3.872983346

Solving
-10 + t = -3.872983346

Solving for variable 't'.

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

Add '10' to each side of the equation.
-10 + 10 + t = -3.872983346 + 10

Combine like terms: -10 + 10 = 0
0 + t = -3.872983346 + 10
t = -3.872983346 + 10

Combine like terms: -3.872983346 + 10 = 6.127016654
t = 6.127016654

Simplifying
t = 6.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.872983346, 6.127016654}
Solution
t = {13.872983346, 6.127016654}

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