16t^2-29t-12=0

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Solution for 16t^2-29t-12=0 equation:


Simplifying
16t2 + -29t + -12 = 0

Reorder the terms:
-12 + -29t + 16t2 = 0

Solving
-12 + -29t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
-0.75 + -1.8125t + t2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -1.8125t + 0.75 + t2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -1.8125t + t2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -1.8125t + t2 = 0 + 0.75
-1.8125t + t2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-1.8125t + t2 = 0.75

The t term is -1.8125t.  Take half its coefficient (-0.90625).
Square it (0.8212890625) and add it to both sides.

Add '0.8212890625' to each side of the equation.
-1.8125t + 0.8212890625 + t2 = 0.75 + 0.8212890625

Reorder the terms:
0.8212890625 + -1.8125t + t2 = 0.75 + 0.8212890625

Combine like terms: 0.75 + 0.8212890625 = 1.5712890625
0.8212890625 + -1.8125t + t2 = 1.5712890625

Factor a perfect square on the left side:
(t + -0.90625)(t + -0.90625) = 1.5712890625

Calculate the square root of the right side: 1.253510695

Break this problem into two subproblems by setting 
(t + -0.90625) equal to 1.253510695 and -1.253510695.

Subproblem 1

t + -0.90625 = 1.253510695 Simplifying t + -0.90625 = 1.253510695 Reorder the terms: -0.90625 + t = 1.253510695 Solving -0.90625 + t = 1.253510695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = 1.253510695 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = 1.253510695 + 0.90625 t = 1.253510695 + 0.90625 Combine like terms: 1.253510695 + 0.90625 = 2.159760695 t = 2.159760695 Simplifying t = 2.159760695

Subproblem 2

t + -0.90625 = -1.253510695 Simplifying t + -0.90625 = -1.253510695 Reorder the terms: -0.90625 + t = -1.253510695 Solving -0.90625 + t = -1.253510695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = -1.253510695 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = -1.253510695 + 0.90625 t = -1.253510695 + 0.90625 Combine like terms: -1.253510695 + 0.90625 = -0.347260695 t = -0.347260695 Simplifying t = -0.347260695

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.159760695, -0.347260695}

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