19=7+29t-16t^2

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Solution for 19=7+29t-16t^2 equation:


Simplifying
19 = 7 + 29t + -16t2

Solving
19 = 7 + 29t + -16t2

Solving for variable 't'.

Combine like terms: 19 + -7 = 12
12 + -29t + 16t2 = 7 + 29t + -16t2 + -7 + -29t + 16t2

Reorder the terms:
12 + -29t + 16t2 = 7 + -7 + 29t + -29t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
12 + -29t + 16t2 = 0 + 29t + -29t + -16t2 + 16t2
12 + -29t + 16t2 = 29t + -29t + -16t2 + 16t2

Combine like terms: 29t + -29t = 0
12 + -29t + 16t2 = 0 + -16t2 + 16t2
12 + -29t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
12 + -29t + 16t2 = 0

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

Divide each side by '16'.
0.75 + -1.8125t + t2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -1.8125t + -0.75 + t2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -1.8125t + t2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -1.8125t + t2 = 0 + -0.75
-1.8125t + t2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-1.8125t + t2 = -0.75

The t term is -1.8125t.  Take half its coefficient (-0.90625).
Square it (0.8212890625) and add it to both sides.

Add '0.8212890625' to each side of the equation.
-1.8125t + 0.8212890625 + t2 = -0.75 + 0.8212890625

Reorder the terms:
0.8212890625 + -1.8125t + t2 = -0.75 + 0.8212890625

Combine like terms: -0.75 + 0.8212890625 = 0.0712890625
0.8212890625 + -1.8125t + t2 = 0.0712890625

Factor a perfect square on the left side:
(t + -0.90625)(t + -0.90625) = 0.0712890625

Calculate the square root of the right side: 0.267000117

Break this problem into two subproblems by setting 
(t + -0.90625) equal to 0.267000117 and -0.267000117.

Subproblem 1

t + -0.90625 = 0.267000117 Simplifying t + -0.90625 = 0.267000117 Reorder the terms: -0.90625 + t = 0.267000117 Solving -0.90625 + t = 0.267000117 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = 0.267000117 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = 0.267000117 + 0.90625 t = 0.267000117 + 0.90625 Combine like terms: 0.267000117 + 0.90625 = 1.173250117 t = 1.173250117 Simplifying t = 1.173250117

Subproblem 2

t + -0.90625 = -0.267000117 Simplifying t + -0.90625 = -0.267000117 Reorder the terms: -0.90625 + t = -0.267000117 Solving -0.90625 + t = -0.267000117 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = -0.267000117 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = -0.267000117 + 0.90625 t = -0.267000117 + 0.90625 Combine like terms: -0.267000117 + 0.90625 = 0.639249883 t = 0.639249883 Simplifying t = 0.639249883

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.173250117, 0.639249883}

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