8t^2+10t-880=980

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Solution for 8t^2+10t-880=980 equation: 


Simplifying
8t2 + 10t + -880 = 980

Reorder the terms:
-880 + 10t + 8t2 = 980

Solving
-880 + 10t + 8t2 = 980

Solving for variable 't'.

Reorder the terms:
-880 + -980 + 10t + 8t2 = 980 + -980

Combine like terms: -880 + -980 = -1860
-1860 + 10t + 8t2 = 980 + -980

Combine like terms: 980 + -980 = 0
-1860 + 10t + 8t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-930 + 5t + 4t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-930 + 5t + 4t2)' equal to zero and attempt to solve:

Simplifying
-930 + 5t + 4t2 = 0

Solving
-930 + 5t + 4t2 = 0

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

Divide each side by '4'.
-232.5 + 1.25t + t2 = 0

Move the constant term to the right:

Add '232.5' to each side of the equation.
-232.5 + 1.25t + 232.5 + t2 = 0 + 232.5

Reorder the terms:
-232.5 + 232.5 + 1.25t + t2 = 0 + 232.5

Combine like terms: -232.5 + 232.5 = 0.0
0.0 + 1.25t + t2 = 0 + 232.5
1.25t + t2 = 0 + 232.5

Combine like terms: 0 + 232.5 = 232.5
1.25t + t2 = 232.5

The t term is 1.25t.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25t + 0.390625 + t2 = 232.5 + 0.390625

Reorder the terms:
0.390625 + 1.25t + t2 = 232.5 + 0.390625

Combine like terms: 232.5 + 0.390625 = 232.890625
0.390625 + 1.25t + t2 = 232.890625

Factor a perfect square on the left side:
(t + 0.625)(t + 0.625) = 232.890625

Calculate the square root of the right side: 15.260754405

Break this problem into two subproblems by setting 
(t + 0.625) equal to 15.260754405 and -15.260754405.


Subproblem 1
t + 0.625 = 15.260754405

Simplifying
t + 0.625 = 15.260754405

Reorder the terms:
0.625 + t = 15.260754405

Solving
0.625 + t = 15.260754405

Solving for variable 't'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + t = 15.260754405 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + t = 15.260754405 + -0.625
t = 15.260754405 + -0.625

Combine like terms: 15.260754405 + -0.625 = 14.635754405
t = 14.635754405

Simplifying
t = 14.635754405


Subproblem 2
t + 0.625 = -15.260754405

Simplifying
t + 0.625 = -15.260754405

Reorder the terms:
0.625 + t = -15.260754405

Solving
0.625 + t = -15.260754405

Solving for variable 't'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + t = -15.260754405 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + t = -15.260754405 + -0.625
t = -15.260754405 + -0.625

Combine like terms: -15.260754405 + -0.625 = -15.885754405
t = -15.885754405

Simplifying
t = -15.885754405


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.635754405, -15.885754405}
Solution
t = {14.635754405, -15.885754405}

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