1.75t^2-30t-100=0

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Solution for 1.75t^2-30t-100=0 equation: 


Simplifying
1.75t2 + -30t + -100 = 0

Reorder the terms:
-100 + -30t + 1.75t2 = 0

Solving
-100 + -30t + 1.75t2 = 0

Solving for variable 't'.

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

Divide each side by '1.75'.
-57.14285714 + -17.14285714t + t2 = 0

Move the constant term to the right:

Add '57.14285714' to each side of the equation.
-57.14285714 + -17.14285714t + 57.14285714 + t2 = 0 + 57.14285714

Reorder the terms:
-57.14285714 + 57.14285714 + -17.14285714t + t2 = 0 + 57.14285714

Combine like terms: -57.14285714 + 57.14285714 = 0.00000000
0.00000000 + -17.14285714t + t2 = 0 + 57.14285714
-17.14285714t + t2 = 0 + 57.14285714

Combine like terms: 0 + 57.14285714 = 57.14285714
-17.14285714t + t2 = 57.14285714

The t term is -17.14285714t.  Take half its coefficient (-8.57142857).
Square it (73.46938773) and add it to both sides.

Add '73.46938773' to each side of the equation.
-17.14285714t + 73.46938773 + t2 = 57.14285714 + 73.46938773

Reorder the terms:
73.46938773 + -17.14285714t + t2 = 57.14285714 + 73.46938773

Combine like terms: 57.14285714 + 73.46938773 = 130.61224487
73.46938773 + -17.14285714t + t2 = 130.61224487

Factor a perfect square on the left side:
(t + -8.57142857)(t + -8.57142857) = 130.61224487

Calculate the square root of the right side: 11.428571427

Break this problem into two subproblems by setting 
(t + -8.57142857) equal to 11.428571427 and -11.428571427.


Subproblem 1
t + -8.57142857 = 11.428571427

Simplifying
t + -8.57142857 = 11.428571427

Reorder the terms:
-8.57142857 + t = 11.428571427

Solving
-8.57142857 + t = 11.428571427

Solving for variable 't'.

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

Add '8.57142857' to each side of the equation.
-8.57142857 + 8.57142857 + t = 11.428571427 + 8.57142857

Combine like terms: -8.57142857 + 8.57142857 = 0.00000000
0.00000000 + t = 11.428571427 + 8.57142857
t = 11.428571427 + 8.57142857

Combine like terms: 11.428571427 + 8.57142857 = 19.999999997
t = 19.999999997

Simplifying
t = 19.999999997


Subproblem 2
t + -8.57142857 = -11.428571427

Simplifying
t + -8.57142857 = -11.428571427

Reorder the terms:
-8.57142857 + t = -11.428571427

Solving
-8.57142857 + t = -11.428571427

Solving for variable 't'.

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

Add '8.57142857' to each side of the equation.
-8.57142857 + 8.57142857 + t = -11.428571427 + 8.57142857

Combine like terms: -8.57142857 + 8.57142857 = 0.00000000
0.00000000 + t = -11.428571427 + 8.57142857
t = -11.428571427 + 8.57142857

Combine like terms: -11.428571427 + 8.57142857 = -2.857142857
t = -2.857142857

Simplifying
t = -2.857142857


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {19.999999997, -2.857142857}

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