17=7+29t-16t^2

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Solution for 17=7+29t-16t^2 equation:


Simplifying
17 = 7 + 29t + -16t2

Solving
17 = 7 + 29t + -16t2

Solving for variable 't'.

Combine like terms: 17 + -7 = 10
10 + -29t + 16t2 = 7 + 29t + -16t2 + -7 + -29t + 16t2

Reorder the terms:
10 + -29t + 16t2 = 7 + -7 + 29t + -29t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
10 + -29t + 16t2 = 0 + 29t + -29t + -16t2 + 16t2
10 + -29t + 16t2 = 29t + -29t + -16t2 + 16t2

Combine like terms: 29t + -29t = 0
10 + -29t + 16t2 = 0 + -16t2 + 16t2
10 + -29t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
10 + -29t + 16t2 = 0

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

Divide each side by '16'.
0.625 + -1.8125t + t2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -1.8125t + -0.625 + t2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -1.8125t + t2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -1.8125t + t2 = 0 + -0.625
-1.8125t + t2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-1.8125t + t2 = -0.625

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 = -0.625 + 0.8212890625

Reorder the terms:
0.8212890625 + -1.8125t + t2 = -0.625 + 0.8212890625

Combine like terms: -0.625 + 0.8212890625 = 0.1962890625
0.8212890625 + -1.8125t + t2 = 0.1962890625

Factor a perfect square on the left side:
(t + -0.90625)(t + -0.90625) = 0.1962890625

Calculate the square root of the right side: 0.443045215

Break this problem into two subproblems by setting 
(t + -0.90625) equal to 0.443045215 and -0.443045215.

Subproblem 1

t + -0.90625 = 0.443045215 Simplifying t + -0.90625 = 0.443045215 Reorder the terms: -0.90625 + t = 0.443045215 Solving -0.90625 + t = 0.443045215 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 = 0.443045215 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = 0.443045215 + 0.90625 t = 0.443045215 + 0.90625 Combine like terms: 0.443045215 + 0.90625 = 1.349295215 t = 1.349295215 Simplifying t = 1.349295215

Subproblem 2

t + -0.90625 = -0.443045215 Simplifying t + -0.90625 = -0.443045215 Reorder the terms: -0.90625 + t = -0.443045215 Solving -0.90625 + t = -0.443045215 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 = -0.443045215 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = -0.443045215 + 0.90625 t = -0.443045215 + 0.90625 Combine like terms: -0.443045215 + 0.90625 = 0.463204785 t = 0.463204785 Simplifying t = 0.463204785

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.349295215, 0.463204785}

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