0=-16t^2+45t+7

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Solution for 0=-16t^2+45t+7 equation:


Simplifying
0 = -16t2 + 45t + 7

Reorder the terms:
0 = 7 + 45t + -16t2

Solving
0 = 7 + 45t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -7 = -7
-7 + -45t + 16t2 = 7 + 45t + -16t2 + -7 + -45t + 16t2

Reorder the terms:
-7 + -45t + 16t2 = 7 + -7 + 45t + -45t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
-7 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2
-7 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2

Combine like terms: 45t + -45t = 0
-7 + -45t + 16t2 = 0 + -16t2 + 16t2
-7 + -45t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-7 + -45t + 16t2 = 0

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

Divide each side by '16'.
-0.4375 + -2.8125t + t2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -2.8125t + 0.4375 + t2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -2.8125t + t2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -2.8125t + t2 = 0 + 0.4375
-2.8125t + t2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-2.8125t + t2 = 0.4375

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 = 0.4375 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125t + t2 = 0.4375 + 1.977539063

Combine like terms: 0.4375 + 1.977539063 = 2.415039063
1.977539063 + -2.8125t + t2 = 2.415039063

Factor a perfect square on the left side:
(t + -1.40625)(t + -1.40625) = 2.415039063

Calculate the square root of the right side: 1.554039595

Break this problem into two subproblems by setting 
(t + -1.40625) equal to 1.554039595 and -1.554039595.

Subproblem 1

t + -1.40625 = 1.554039595 Simplifying t + -1.40625 = 1.554039595 Reorder the terms: -1.40625 + t = 1.554039595 Solving -1.40625 + t = 1.554039595 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 = 1.554039595 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.554039595 + 1.40625 t = 1.554039595 + 1.40625 Combine like terms: 1.554039595 + 1.40625 = 2.960289595 t = 2.960289595 Simplifying t = 2.960289595

Subproblem 2

t + -1.40625 = -1.554039595 Simplifying t + -1.40625 = -1.554039595 Reorder the terms: -1.40625 + t = -1.554039595 Solving -1.40625 + t = -1.554039595 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 = -1.554039595 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.554039595 + 1.40625 t = -1.554039595 + 1.40625 Combine like terms: -1.554039595 + 1.40625 = -0.147789595 t = -0.147789595 Simplifying t = -0.147789595

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.960289595, -0.147789595}

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