2=-32t^2+8t+3

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Solution for 2=-32t^2+8t+3 equation:


Simplifying
2 = -32t2 + 8t + 3

Reorder the terms:
2 = 3 + 8t + -32t2

Solving
2 = 3 + 8t + -32t2

Solving for variable 't'.

Combine like terms: 2 + -3 = -1
-1 + -8t + 32t2 = 3 + 8t + -32t2 + -3 + -8t + 32t2

Reorder the terms:
-1 + -8t + 32t2 = 3 + -3 + 8t + -8t + -32t2 + 32t2

Combine like terms: 3 + -3 = 0
-1 + -8t + 32t2 = 0 + 8t + -8t + -32t2 + 32t2
-1 + -8t + 32t2 = 8t + -8t + -32t2 + 32t2

Combine like terms: 8t + -8t = 0
-1 + -8t + 32t2 = 0 + -32t2 + 32t2
-1 + -8t + 32t2 = -32t2 + 32t2

Combine like terms: -32t2 + 32t2 = 0
-1 + -8t + 32t2 = 0

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

Divide each side by '32'.
-0.03125 + -0.25t + t2 = 0

Move the constant term to the right:

Add '0.03125' to each side of the equation.
-0.03125 + -0.25t + 0.03125 + t2 = 0 + 0.03125

Reorder the terms:
-0.03125 + 0.03125 + -0.25t + t2 = 0 + 0.03125

Combine like terms: -0.03125 + 0.03125 = 0.00000
0.00000 + -0.25t + t2 = 0 + 0.03125
-0.25t + t2 = 0 + 0.03125

Combine like terms: 0 + 0.03125 = 0.03125
-0.25t + t2 = 0.03125

The t term is -0.25t.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25t + 0.015625 + t2 = 0.03125 + 0.015625

Reorder the terms:
0.015625 + -0.25t + t2 = 0.03125 + 0.015625

Combine like terms: 0.03125 + 0.015625 = 0.046875
0.015625 + -0.25t + t2 = 0.046875

Factor a perfect square on the left side:
(t + -0.125)(t + -0.125) = 0.046875

Calculate the square root of the right side: 0.216506351

Break this problem into two subproblems by setting 
(t + -0.125) equal to 0.216506351 and -0.216506351.

Subproblem 1

t + -0.125 = 0.216506351 Simplifying t + -0.125 = 0.216506351 Reorder the terms: -0.125 + t = 0.216506351 Solving -0.125 + t = 0.216506351 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 0.216506351 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 0.216506351 + 0.125 t = 0.216506351 + 0.125 Combine like terms: 0.216506351 + 0.125 = 0.341506351 t = 0.341506351 Simplifying t = 0.341506351

Subproblem 2

t + -0.125 = -0.216506351 Simplifying t + -0.125 = -0.216506351 Reorder the terms: -0.125 + t = -0.216506351 Solving -0.125 + t = -0.216506351 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -0.216506351 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -0.216506351 + 0.125 t = -0.216506351 + 0.125 Combine like terms: -0.216506351 + 0.125 = -0.091506351 t = -0.091506351 Simplifying t = -0.091506351

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.341506351, -0.091506351}

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