0=-16t^2+45t-25

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Solution for 0=-16t^2+45t-25 equation:


Simplifying
0 = -16t2 + 45t + -25

Reorder the terms:
0 = -25 + 45t + -16t2

Solving
0 = -25 + 45t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 25 = 25
25 + -45t + 16t2 = -25 + 45t + -16t2 + 25 + -45t + 16t2

Reorder the terms:
25 + -45t + 16t2 = -25 + 25 + 45t + -45t + -16t2 + 16t2

Combine like terms: -25 + 25 = 0
25 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2
25 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2

Combine like terms: 45t + -45t = 0
25 + -45t + 16t2 = 0 + -16t2 + 16t2
25 + -45t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
25 + -45t + 16t2 = 0

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

Divide each side by '16'.
1.5625 + -2.8125t + t2 = 0

Move the constant term to the right:

Add '-1.5625' to each side of the equation.
1.5625 + -2.8125t + -1.5625 + t2 = 0 + -1.5625

Reorder the terms:
1.5625 + -1.5625 + -2.8125t + t2 = 0 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + -2.8125t + t2 = 0 + -1.5625
-2.8125t + t2 = 0 + -1.5625

Combine like terms: 0 + -1.5625 = -1.5625
-2.8125t + t2 = -1.5625

The t term is -2.8125t.  Take half its coefficient (-1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
-2.8125t + 1.977539063 + t2 = -1.5625 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125t + t2 = -1.5625 + 1.977539063

Combine like terms: -1.5625 + 1.977539063 = 0.415039063
1.977539063 + -2.8125t + t2 = 0.415039063

Factor a perfect square on the left side:
(t + -1.40625)(t + -1.40625) = 0.415039063

Calculate the square root of the right side: 0.644235254

Break this problem into two subproblems by setting 
(t + -1.40625) equal to 0.644235254 and -0.644235254.

Subproblem 1

t + -1.40625 = 0.644235254 Simplifying t + -1.40625 = 0.644235254 Reorder the terms: -1.40625 + t = 0.644235254 Solving -1.40625 + t = 0.644235254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 0.644235254 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 0.644235254 + 1.40625 t = 0.644235254 + 1.40625 Combine like terms: 0.644235254 + 1.40625 = 2.050485254 t = 2.050485254 Simplifying t = 2.050485254

Subproblem 2

t + -1.40625 = -0.644235254 Simplifying t + -1.40625 = -0.644235254 Reorder the terms: -1.40625 + t = -0.644235254 Solving -1.40625 + t = -0.644235254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -0.644235254 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -0.644235254 + 1.40625 t = -0.644235254 + 1.40625 Combine like terms: -0.644235254 + 1.40625 = 0.762014746 t = 0.762014746 Simplifying t = 0.762014746

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.050485254, 0.762014746}

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