-16t^2+126t=126+5

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Solution for -16t^2+126t=126+5 equation: 


Simplifying
-16t2 + 126t = 126 + 5

Reorder the terms:
126t + -16t2 = 126 + 5

Combine like terms: 126 + 5 = 131
126t + -16t2 = 131

Solving
126t + -16t2 = 131

Solving for variable 't'.

Reorder the terms:
-131 + 126t + -16t2 = 131 + -131

Combine like terms: 131 + -131 = 0
-131 + 126t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
8.1875 + -7.875t + t2 = 0

Move the constant term to the right:

Add '-8.1875' to each side of the equation.
8.1875 + -7.875t + -8.1875 + t2 = 0 + -8.1875

Reorder the terms:
8.1875 + -8.1875 + -7.875t + t2 = 0 + -8.1875

Combine like terms: 8.1875 + -8.1875 = 0.0000
0.0000 + -7.875t + t2 = 0 + -8.1875
-7.875t + t2 = 0 + -8.1875

Combine like terms: 0 + -8.1875 = -8.1875
-7.875t + t2 = -8.1875

The t term is -7.875t.  Take half its coefficient (-3.9375).
Square it (15.50390625) and add it to both sides.

Add '15.50390625' to each side of the equation.
-7.875t + 15.50390625 + t2 = -8.1875 + 15.50390625

Reorder the terms:
15.50390625 + -7.875t + t2 = -8.1875 + 15.50390625

Combine like terms: -8.1875 + 15.50390625 = 7.31640625
15.50390625 + -7.875t + t2 = 7.31640625

Factor a perfect square on the left side:
(t + -3.9375)(t + -3.9375) = 7.31640625

Calculate the square root of the right side: 2.704885626

Break this problem into two subproblems by setting 
(t + -3.9375) equal to 2.704885626 and -2.704885626.


Subproblem 1
t + -3.9375 = 2.704885626

Simplifying
t + -3.9375 = 2.704885626

Reorder the terms:
-3.9375 + t = 2.704885626

Solving
-3.9375 + t = 2.704885626

Solving for variable 't'.

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

Add '3.9375' to each side of the equation.
-3.9375 + 3.9375 + t = 2.704885626 + 3.9375

Combine like terms: -3.9375 + 3.9375 = 0.0000
0.0000 + t = 2.704885626 + 3.9375
t = 2.704885626 + 3.9375

Combine like terms: 2.704885626 + 3.9375 = 6.642385626
t = 6.642385626

Simplifying
t = 6.642385626


Subproblem 2
t + -3.9375 = -2.704885626

Simplifying
t + -3.9375 = -2.704885626

Reorder the terms:
-3.9375 + t = -2.704885626

Solving
-3.9375 + t = -2.704885626

Solving for variable 't'.

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

Add '3.9375' to each side of the equation.
-3.9375 + 3.9375 + t = -2.704885626 + 3.9375

Combine like terms: -3.9375 + 3.9375 = 0.0000
0.0000 + t = -2.704885626 + 3.9375
t = -2.704885626 + 3.9375

Combine like terms: -2.704885626 + 3.9375 = 1.232614374
t = 1.232614374

Simplifying
t = 1.232614374


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.642385626, 1.232614374}

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