150=-16t^2+117t+2

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Solution for 150=-16t^2+117t+2 equation:


Simplifying
150 = -16t2 + 117t + 2

Reorder the terms:
150 = 2 + 117t + -16t2

Solving
150 = 2 + 117t + -16t2

Solving for variable 't'.

Combine like terms: 150 + -2 = 148
148 + -117t + 16t2 = 2 + 117t + -16t2 + -2 + -117t + 16t2

Reorder the terms:
148 + -117t + 16t2 = 2 + -2 + 117t + -117t + -16t2 + 16t2

Combine like terms: 2 + -2 = 0
148 + -117t + 16t2 = 0 + 117t + -117t + -16t2 + 16t2
148 + -117t + 16t2 = 117t + -117t + -16t2 + 16t2

Combine like terms: 117t + -117t = 0
148 + -117t + 16t2 = 0 + -16t2 + 16t2
148 + -117t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
148 + -117t + 16t2 = 0

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

Divide each side by '16'.
9.25 + -7.3125t + t2 = 0

Move the constant term to the right:

Add '-9.25' to each side of the equation.
9.25 + -7.3125t + -9.25 + t2 = 0 + -9.25

Reorder the terms:
9.25 + -9.25 + -7.3125t + t2 = 0 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + -7.3125t + t2 = 0 + -9.25
-7.3125t + t2 = 0 + -9.25

Combine like terms: 0 + -9.25 = -9.25
-7.3125t + t2 = -9.25

The t term is -7.3125t.  Take half its coefficient (-3.65625).
Square it (13.36816406) and add it to both sides.

Add '13.36816406' to each side of the equation.
-7.3125t + 13.36816406 + t2 = -9.25 + 13.36816406

Reorder the terms:
13.36816406 + -7.3125t + t2 = -9.25 + 13.36816406

Combine like terms: -9.25 + 13.36816406 = 4.11816406
13.36816406 + -7.3125t + t2 = 4.11816406

Factor a perfect square on the left side:
(t + -3.65625)(t + -3.65625) = 4.11816406

Calculate the square root of the right side: 2.029326011

Break this problem into two subproblems by setting 
(t + -3.65625) equal to 2.029326011 and -2.029326011.

Subproblem 1

t + -3.65625 = 2.029326011 Simplifying t + -3.65625 = 2.029326011 Reorder the terms: -3.65625 + t = 2.029326011 Solving -3.65625 + t = 2.029326011 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = 2.029326011 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = 2.029326011 + 3.65625 t = 2.029326011 + 3.65625 Combine like terms: 2.029326011 + 3.65625 = 5.685576011 t = 5.685576011 Simplifying t = 5.685576011

Subproblem 2

t + -3.65625 = -2.029326011 Simplifying t + -3.65625 = -2.029326011 Reorder the terms: -3.65625 + t = -2.029326011 Solving -3.65625 + t = -2.029326011 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = -2.029326011 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = -2.029326011 + 3.65625 t = -2.029326011 + 3.65625 Combine like terms: -2.029326011 + 3.65625 = 1.626923989 t = 1.626923989 Simplifying t = 1.626923989

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.685576011, 1.626923989}

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