-16t^2+40t+2.5=0

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Solution for -16t^2+40t+2.5=0 equation:


Simplifying
-16t2 + 40t + 2.5 = 0

Reorder the terms:
2.5 + 40t + -16t2 = 0

Solving
2.5 + 40t + -16t2 = 0

Solving for variable 't'.

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

Divide each side by '-16'.
-0.15625 + -2.5t + t2 = 0

Move the constant term to the right:

Add '0.15625' to each side of the equation.
-0.15625 + -2.5t + 0.15625 + t2 = 0 + 0.15625

Reorder the terms:
-0.15625 + 0.15625 + -2.5t + t2 = 0 + 0.15625

Combine like terms: -0.15625 + 0.15625 = 0.00000
0.00000 + -2.5t + t2 = 0 + 0.15625
-2.5t + t2 = 0 + 0.15625

Combine like terms: 0 + 0.15625 = 0.15625
-2.5t + t2 = 0.15625

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = 0.15625 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = 0.15625 + 1.5625

Combine like terms: 0.15625 + 1.5625 = 1.71875
1.5625 + -2.5t + t2 = 1.71875

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 1.71875

Calculate the square root of the right side: 1.31101106

Break this problem into two subproblems by setting 
(t + -1.25) equal to 1.31101106 and -1.31101106.

Subproblem 1

t + -1.25 = 1.31101106 Simplifying t + -1.25 = 1.31101106 Reorder the terms: -1.25 + t = 1.31101106 Solving -1.25 + t = 1.31101106 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 1.31101106 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.31101106 + 1.25 t = 1.31101106 + 1.25 Combine like terms: 1.31101106 + 1.25 = 2.56101106 t = 2.56101106 Simplifying t = 2.56101106

Subproblem 2

t + -1.25 = -1.31101106 Simplifying t + -1.25 = -1.31101106 Reorder the terms: -1.25 + t = -1.31101106 Solving -1.25 + t = -1.31101106 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -1.31101106 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.31101106 + 1.25 t = -1.31101106 + 1.25 Combine like terms: -1.31101106 + 1.25 = -0.06101106 t = -0.06101106 Simplifying t = -0.06101106

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.56101106, -0.06101106}

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