-7=29t-16t^2

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


Simplifying
-7 = 29t + -16t2

Solving
-7 = 29t + -16t2

Solving for variable 't'.

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

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

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

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

Divide each side by '16'.
-0.4375 + -1.8125t + t2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -1.8125t + 0.4375 + t2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -1.8125t + t2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -1.8125t + t2 = 0 + 0.4375
-1.8125t + t2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-1.8125t + t2 = 0.4375

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 = 0.4375 + 0.8212890625

Reorder the terms:
0.8212890625 + -1.8125t + t2 = 0.4375 + 0.8212890625

Combine like terms: 0.4375 + 0.8212890625 = 1.2587890625
0.8212890625 + -1.8125t + t2 = 1.2587890625

Factor a perfect square on the left side:
(t + -0.90625)(t + -0.90625) = 1.2587890625

Calculate the square root of the right side: 1.121957692

Break this problem into two subproblems by setting 
(t + -0.90625) equal to 1.121957692 and -1.121957692.

Subproblem 1

t + -0.90625 = 1.121957692 Simplifying t + -0.90625 = 1.121957692 Reorder the terms: -0.90625 + t = 1.121957692 Solving -0.90625 + t = 1.121957692 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 = 1.121957692 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = 1.121957692 + 0.90625 t = 1.121957692 + 0.90625 Combine like terms: 1.121957692 + 0.90625 = 2.028207692 t = 2.028207692 Simplifying t = 2.028207692

Subproblem 2

t + -0.90625 = -1.121957692 Simplifying t + -0.90625 = -1.121957692 Reorder the terms: -0.90625 + t = -1.121957692 Solving -0.90625 + t = -1.121957692 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 = -1.121957692 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = -1.121957692 + 0.90625 t = -1.121957692 + 0.90625 Combine like terms: -1.121957692 + 0.90625 = -0.215707692 t = -0.215707692 Simplifying t = -0.215707692

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.028207692, -0.215707692}

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