0=-16t^2+118t+3

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Solution for 0=-16t^2+118t+3 equation:


Simplifying
0 = -16t2 + 118t + 3

Reorder the terms:
0 = 3 + 118t + -16t2

Solving
0 = 3 + 118t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -118t + 16t2 = 3 + 118t + -16t2 + -3 + -118t + 16t2

Reorder the terms:
-3 + -118t + 16t2 = 3 + -3 + 118t + -118t + -16t2 + 16t2

Combine like terms: 3 + -3 = 0
-3 + -118t + 16t2 = 0 + 118t + -118t + -16t2 + 16t2
-3 + -118t + 16t2 = 118t + -118t + -16t2 + 16t2

Combine like terms: 118t + -118t = 0
-3 + -118t + 16t2 = 0 + -16t2 + 16t2
-3 + -118t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-3 + -118t + 16t2 = 0

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

Divide each side by '16'.
-0.1875 + -7.375t + t2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -7.375t + 0.1875 + t2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -7.375t + t2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -7.375t + t2 = 0 + 0.1875
-7.375t + t2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-7.375t + t2 = 0.1875

The t term is -7.375t.  Take half its coefficient (-3.6875).
Square it (13.59765625) and add it to both sides.

Add '13.59765625' to each side of the equation.
-7.375t + 13.59765625 + t2 = 0.1875 + 13.59765625

Reorder the terms:
13.59765625 + -7.375t + t2 = 0.1875 + 13.59765625

Combine like terms: 0.1875 + 13.59765625 = 13.78515625
13.59765625 + -7.375t + t2 = 13.78515625

Factor a perfect square on the left side:
(t + -3.6875)(t + -3.6875) = 13.78515625

Calculate the square root of the right side: 3.712836685

Break this problem into two subproblems by setting 
(t + -3.6875) equal to 3.712836685 and -3.712836685.

Subproblem 1

t + -3.6875 = 3.712836685 Simplifying t + -3.6875 = 3.712836685 Reorder the terms: -3.6875 + t = 3.712836685 Solving -3.6875 + t = 3.712836685 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + t = 3.712836685 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + t = 3.712836685 + 3.6875 t = 3.712836685 + 3.6875 Combine like terms: 3.712836685 + 3.6875 = 7.400336685 t = 7.400336685 Simplifying t = 7.400336685

Subproblem 2

t + -3.6875 = -3.712836685 Simplifying t + -3.6875 = -3.712836685 Reorder the terms: -3.6875 + t = -3.712836685 Solving -3.6875 + t = -3.712836685 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + t = -3.712836685 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + t = -3.712836685 + 3.6875 t = -3.712836685 + 3.6875 Combine like terms: -3.712836685 + 3.6875 = -0.025336685 t = -0.025336685 Simplifying t = -0.025336685

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.400336685, -0.025336685}

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