4t^2-25t-15=0

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Solution for 4t^2-25t-15=0 equation: 


Simplifying
4t2 + -25t + -15 = 0

Reorder the terms:
-15 + -25t + 4t2 = 0

Solving
-15 + -25t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-3.75 + -6.25t + t2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -6.25t + 3.75 + t2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -6.25t + t2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -6.25t + t2 = 0 + 3.75
-6.25t + t2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-6.25t + t2 = 3.75

The t term is -6.25t.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25t + 9.765625 + t2 = 3.75 + 9.765625

Reorder the terms:
9.765625 + -6.25t + t2 = 3.75 + 9.765625

Combine like terms: 3.75 + 9.765625 = 13.515625
9.765625 + -6.25t + t2 = 13.515625

Factor a perfect square on the left side:
(t + -3.125)(t + -3.125) = 13.515625

Calculate the square root of the right side: 3.676360292

Break this problem into two subproblems by setting 
(t + -3.125) equal to 3.676360292 and -3.676360292.


Subproblem 1
t + -3.125 = 3.676360292

Simplifying
t + -3.125 = 3.676360292

Reorder the terms:
-3.125 + t = 3.676360292

Solving
-3.125 + t = 3.676360292

Solving for variable 't'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + t = 3.676360292 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = 3.676360292 + 3.125
t = 3.676360292 + 3.125

Combine like terms: 3.676360292 + 3.125 = 6.801360292
t = 6.801360292

Simplifying
t = 6.801360292


Subproblem 2
t + -3.125 = -3.676360292

Simplifying
t + -3.125 = -3.676360292

Reorder the terms:
-3.125 + t = -3.676360292

Solving
-3.125 + t = -3.676360292

Solving for variable 't'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + t = -3.676360292 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = -3.676360292 + 3.125
t = -3.676360292 + 3.125

Combine like terms: -3.676360292 + 3.125 = -0.551360292
t = -0.551360292

Simplifying
t = -0.551360292


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.801360292, -0.551360292}

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