0=-16t^2+12t+11

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Solution for 0=-16t^2+12t+11 equation:


Simplifying
0 = -16t2 + 12t + 11

Reorder the terms:
0 = 11 + 12t + -16t2

Solving
0 = 11 + 12t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -11 = -11
-11 + -12t + 16t2 = 11 + 12t + -16t2 + -11 + -12t + 16t2

Reorder the terms:
-11 + -12t + 16t2 = 11 + -11 + 12t + -12t + -16t2 + 16t2

Combine like terms: 11 + -11 = 0
-11 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2
-11 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2

Combine like terms: 12t + -12t = 0
-11 + -12t + 16t2 = 0 + -16t2 + 16t2
-11 + -12t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-11 + -12t + 16t2 = 0

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

Divide each side by '16'.
-0.6875 + -0.75t + t2 = 0

Move the constant term to the right:

Add '0.6875' to each side of the equation.
-0.6875 + -0.75t + 0.6875 + t2 = 0 + 0.6875

Reorder the terms:
-0.6875 + 0.6875 + -0.75t + t2 = 0 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + -0.75t + t2 = 0 + 0.6875
-0.75t + t2 = 0 + 0.6875

Combine like terms: 0 + 0.6875 = 0.6875
-0.75t + t2 = 0.6875

The t term is -0.75t.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75t + 0.140625 + t2 = 0.6875 + 0.140625

Reorder the terms:
0.140625 + -0.75t + t2 = 0.6875 + 0.140625

Combine like terms: 0.6875 + 0.140625 = 0.828125
0.140625 + -0.75t + t2 = 0.828125

Factor a perfect square on the left side:
(t + -0.375)(t + -0.375) = 0.828125

Calculate the square root of the right side: 0.910013736

Break this problem into two subproblems by setting 
(t + -0.375) equal to 0.910013736 and -0.910013736.

Subproblem 1

t + -0.375 = 0.910013736 Simplifying t + -0.375 = 0.910013736 Reorder the terms: -0.375 + t = 0.910013736 Solving -0.375 + t = 0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 0.910013736 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 0.910013736 + 0.375 t = 0.910013736 + 0.375 Combine like terms: 0.910013736 + 0.375 = 1.285013736 t = 1.285013736 Simplifying t = 1.285013736

Subproblem 2

t + -0.375 = -0.910013736 Simplifying t + -0.375 = -0.910013736 Reorder the terms: -0.375 + t = -0.910013736 Solving -0.375 + t = -0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -0.910013736 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -0.910013736 + 0.375 t = -0.910013736 + 0.375 Combine like terms: -0.910013736 + 0.375 = -0.535013736 t = -0.535013736 Simplifying t = -0.535013736

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.285013736, -0.535013736}

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