-16t^2+12t=-5

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Solution for -16t^2+12t=-5 equation:


Simplifying
-16t2 + 12t = -5

Reorder the terms:
12t + -16t2 = -5

Solving
12t + -16t2 = -5

Solving for variable 't'.

Reorder the terms:
5 + 12t + -16t2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 12t + -16t2 = 0

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

Divide each side by '-16'.
-0.3125 + -0.75t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -0.75t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -0.75t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -0.75t + t2 = 0 + 0.3125
-0.75t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-0.75t + t2 = 0.3125

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 = 0.3125 + 0.140625

Reorder the terms:
0.140625 + -0.75t + t2 = 0.3125 + 0.140625

Combine like terms: 0.3125 + 0.140625 = 0.453125
0.140625 + -0.75t + t2 = 0.453125

Factor a perfect square on the left side:
(t + -0.375)(t + -0.375) = 0.453125

Calculate the square root of the right side: 0.673145601

Break this problem into two subproblems by setting 
(t + -0.375) equal to 0.673145601 and -0.673145601.

Subproblem 1

t + -0.375 = 0.673145601 Simplifying t + -0.375 = 0.673145601 Reorder the terms: -0.375 + t = 0.673145601 Solving -0.375 + t = 0.673145601 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 = 0.673145601 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 0.673145601 + 0.375 t = 0.673145601 + 0.375 Combine like terms: 0.673145601 + 0.375 = 1.048145601 t = 1.048145601 Simplifying t = 1.048145601

Subproblem 2

t + -0.375 = -0.673145601 Simplifying t + -0.375 = -0.673145601 Reorder the terms: -0.375 + t = -0.673145601 Solving -0.375 + t = -0.673145601 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 = -0.673145601 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -0.673145601 + 0.375 t = -0.673145601 + 0.375 Combine like terms: -0.673145601 + 0.375 = -0.298145601 t = -0.298145601 Simplifying t = -0.298145601

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.048145601, -0.298145601}

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