0=-2.25+13t-16t^2

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Solution for 0=-2.25+13t-16t^2 equation:


Simplifying
0 = -2.25 + 13t + -16t2

Solving
0 = -2.25 + 13t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 2.25 = 2.25
2.25 + -13t + 16t2 = -2.25 + 13t + -16t2 + 2.25 + -13t + 16t2

Reorder the terms:
2.25 + -13t + 16t2 = -2.25 + 2.25 + 13t + -13t + -16t2 + 16t2

Combine like terms: -2.25 + 2.25 = 0.00
2.25 + -13t + 16t2 = 0.00 + 13t + -13t + -16t2 + 16t2
2.25 + -13t + 16t2 = 13t + -13t + -16t2 + 16t2

Combine like terms: 13t + -13t = 0
2.25 + -13t + 16t2 = 0 + -16t2 + 16t2
2.25 + -13t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
2.25 + -13t + 16t2 = 0

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

Divide each side by '16'.
0.140625 + -0.8125t + t2 = 0

Move the constant term to the right:

Add '-0.140625' to each side of the equation.
0.140625 + -0.8125t + -0.140625 + t2 = 0 + -0.140625

Reorder the terms:
0.140625 + -0.140625 + -0.8125t + t2 = 0 + -0.140625

Combine like terms: 0.140625 + -0.140625 = 0.000000
0.000000 + -0.8125t + t2 = 0 + -0.140625
-0.8125t + t2 = 0 + -0.140625

Combine like terms: 0 + -0.140625 = -0.140625
-0.8125t + t2 = -0.140625

The t term is -0.8125t.  Take half its coefficient (-0.40625).
Square it (0.1650390625) and add it to both sides.

Add '0.1650390625' to each side of the equation.
-0.8125t + 0.1650390625 + t2 = -0.140625 + 0.1650390625

Reorder the terms:
0.1650390625 + -0.8125t + t2 = -0.140625 + 0.1650390625

Combine like terms: -0.140625 + 0.1650390625 = 0.0244140625
0.1650390625 + -0.8125t + t2 = 0.0244140625

Factor a perfect square on the left side:
(t + -0.40625)(t + -0.40625) = 0.0244140625

Calculate the square root of the right side: 0.15625

Break this problem into two subproblems by setting 
(t + -0.40625) equal to 0.15625 and -0.15625.

Subproblem 1

t + -0.40625 = 0.15625 Simplifying t + -0.40625 = 0.15625 Reorder the terms: -0.40625 + t = 0.15625 Solving -0.40625 + t = 0.15625 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + t = 0.15625 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = 0.15625 + 0.40625 t = 0.15625 + 0.40625 Combine like terms: 0.15625 + 0.40625 = 0.5625 t = 0.5625 Simplifying t = 0.5625

Subproblem 2

t + -0.40625 = -0.15625 Simplifying t + -0.40625 = -0.15625 Reorder the terms: -0.40625 + t = -0.15625 Solving -0.40625 + t = -0.15625 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + t = -0.15625 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = -0.15625 + 0.40625 t = -0.15625 + 0.40625 Combine like terms: -0.15625 + 0.40625 = 0.25 t = 0.25 Simplifying t = 0.25

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.5625, 0.25}

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