t-9=28t^2-37t-225

Solution for t-9=28t^2-37t-225 equation:

Simplifying
t + -9 = 28t2 + -37t + -225

Reorder the terms:
-9 + t = 28t2 + -37t + -225

Reorder the terms:
-9 + t = -225 + -37t + 28t2

Solving
-9 + t = -225 + -37t + 28t2

Solving for variable 't'.

Reorder the terms:
-9 + 225 + t + 37t + -28t2 = -225 + -37t + 28t2 + 225 + 37t + -28t2

Combine like terms: -9 + 225 = 216
216 + t + 37t + -28t2 = -225 + -37t + 28t2 + 225 + 37t + -28t2

Combine like terms: t + 37t = 38t
216 + 38t + -28t2 = -225 + -37t + 28t2 + 225 + 37t + -28t2

Reorder the terms:
216 + 38t + -28t2 = -225 + 225 + -37t + 37t + 28t2 + -28t2

Combine like terms: -225 + 225 = 0
216 + 38t + -28t2 = 0 + -37t + 37t + 28t2 + -28t2
216 + 38t + -28t2 = -37t + 37t + 28t2 + -28t2

Combine like terms: -37t + 37t = 0
216 + 38t + -28t2 = 0 + 28t2 + -28t2
216 + 38t + -28t2 = 28t2 + -28t2

Combine like terms: 28t2 + -28t2 = 0
216 + 38t + -28t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + 19t + -14t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(108 + 19t + -14t2)' equal to zero and attempt to solve:

Simplifying
108 + 19t + -14t2 = 0

Solving
108 + 19t + -14t2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-7.714285714 + -1.357142857t + t2 = 0

Move the constant term to the right:

Add '7.714285714' to each side of the equation.
-7.714285714 + -1.357142857t + 7.714285714 + t2 = 0 + 7.714285714

Reorder the terms:
-7.714285714 + 7.714285714 + -1.357142857t + t2 = 0 + 7.714285714

Combine like terms: -7.714285714 + 7.714285714 = 0.000000000
0.000000000 + -1.357142857t + t2 = 0 + 7.714285714
-1.357142857t + t2 = 0 + 7.714285714

Combine like terms: 0 + 7.714285714 = 7.714285714
-1.357142857t + t2 = 7.714285714

The t term is -1.357142857t.  Take half its coefficient (-0.6785714285).
Square it (0.4604591836) and add it to both sides.

Add '0.4604591836' to each side of the equation.
-1.357142857t + 0.4604591836 + t2 = 7.714285714 + 0.4604591836

Reorder the terms:
0.4604591836 + -1.357142857t + t2 = 7.714285714 + 0.4604591836

Combine like terms: 7.714285714 + 0.4604591836 = 8.1747448976
0.4604591836 + -1.357142857t + t2 = 8.1747448976

Factor a perfect square on the left side:
(t + -0.6785714285)(t + -0.6785714285) = 8.1747448976

Calculate the square root of the right side: 2.85915108

Break this problem into two subproblems by setting 
(t + -0.6785714285) equal to 2.85915108 and -2.85915108.

Subproblem 1
t + -0.6785714285 = 2.85915108

Simplifying
t + -0.6785714285 = 2.85915108

Reorder the terms:
-0.6785714285 + t = 2.85915108

Solving
-0.6785714285 + t = 2.85915108

Solving for variable 't'.

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

Add '0.6785714285' to each side of the equation.
-0.6785714285 + 0.6785714285 + t = 2.85915108 + 0.6785714285

Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000
0.0000000000 + t = 2.85915108 + 0.6785714285
t = 2.85915108 + 0.6785714285

Combine like terms: 2.85915108 + 0.6785714285 = 3.5377225085
t = 3.5377225085

Simplifying
t = 3.5377225085

Subproblem 2
t + -0.6785714285 = -2.85915108

Simplifying
t + -0.6785714285 = -2.85915108

Reorder the terms:
-0.6785714285 + t = -2.85915108

Solving
-0.6785714285 + t = -2.85915108

Solving for variable 't'.

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

Add '0.6785714285' to each side of the equation.
-0.6785714285 + 0.6785714285 + t = -2.85915108 + 0.6785714285

Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000
0.0000000000 + t = -2.85915108 + 0.6785714285
t = -2.85915108 + 0.6785714285

Combine like terms: -2.85915108 + 0.6785714285 = -2.1805796515
t = -2.1805796515

Simplifying
t = -2.1805796515

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.5377225085, -2.1805796515}
Solution
t = {3.5377225085, -2.1805796515}