2*t^2-25*t-100=0

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Solution for 2*t^2-25*t-100=0 equation:


Simplifying
2t2 + -25t + -100 = 0

Reorder the terms:
-100 + -25t + 2t2 = 0

Solving
-100 + -25t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
-50 + -12.5t + t2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -12.5t + 50 + t2 = 0 + 50

Reorder the terms:
-50 + 50 + -12.5t + t2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -12.5t + t2 = 0 + 50
-12.5t + t2 = 0 + 50

Combine like terms: 0 + 50 = 50
-12.5t + t2 = 50

The t term is -12.5t.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5t + 39.0625 + t2 = 50 + 39.0625

Reorder the terms:
39.0625 + -12.5t + t2 = 50 + 39.0625

Combine like terms: 50 + 39.0625 = 89.0625
39.0625 + -12.5t + t2 = 89.0625

Factor a perfect square on the left side:
(t + -6.25)(t + -6.25) = 89.0625

Calculate the square root of the right side: 9.437293044

Break this problem into two subproblems by setting 
(t + -6.25) equal to 9.437293044 and -9.437293044.

Subproblem 1

t + -6.25 = 9.437293044 Simplifying t + -6.25 = 9.437293044 Reorder the terms: -6.25 + t = 9.437293044 Solving -6.25 + t = 9.437293044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = 9.437293044 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 9.437293044 + 6.25 t = 9.437293044 + 6.25 Combine like terms: 9.437293044 + 6.25 = 15.687293044 t = 15.687293044 Simplifying t = 15.687293044

Subproblem 2

t + -6.25 = -9.437293044 Simplifying t + -6.25 = -9.437293044 Reorder the terms: -6.25 + t = -9.437293044 Solving -6.25 + t = -9.437293044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = -9.437293044 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -9.437293044 + 6.25 t = -9.437293044 + 6.25 Combine like terms: -9.437293044 + 6.25 = -3.187293044 t = -3.187293044 Simplifying t = -3.187293044

Solution

The solution to the problem is based on the solutions from the subproblems. t = {15.687293044, -3.187293044}

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