16t^2-25t-3=0

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Solution for 16t^2-25t-3=0 equation:


Simplifying
16t2 + -25t + -3 = 0

Reorder the terms:
-3 + -25t + 16t2 = 0

Solving
-3 + -25t + 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'.
-0.1875 + -1.5625t + t2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -1.5625t + 0.1875 + t2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -1.5625t + t2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -1.5625t + t2 = 0 + 0.1875
-1.5625t + t2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-1.5625t + t2 = 0.1875

The t term is -1.5625t.  Take half its coefficient (-0.78125).
Square it (0.6103515625) and add it to both sides.

Add '0.6103515625' to each side of the equation.
-1.5625t + 0.6103515625 + t2 = 0.1875 + 0.6103515625

Reorder the terms:
0.6103515625 + -1.5625t + t2 = 0.1875 + 0.6103515625

Combine like terms: 0.1875 + 0.6103515625 = 0.7978515625
0.6103515625 + -1.5625t + t2 = 0.7978515625

Factor a perfect square on the left side:
(t + -0.78125)(t + -0.78125) = 0.7978515625

Calculate the square root of the right side: 0.89322537

Break this problem into two subproblems by setting 
(t + -0.78125) equal to 0.89322537 and -0.89322537.

Subproblem 1

t + -0.78125 = 0.89322537 Simplifying t + -0.78125 = 0.89322537 Reorder the terms: -0.78125 + t = 0.89322537 Solving -0.78125 + t = 0.89322537 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 0.89322537 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 0.89322537 + 0.78125 t = 0.89322537 + 0.78125 Combine like terms: 0.89322537 + 0.78125 = 1.67447537 t = 1.67447537 Simplifying t = 1.67447537

Subproblem 2

t + -0.78125 = -0.89322537 Simplifying t + -0.78125 = -0.89322537 Reorder the terms: -0.78125 + t = -0.89322537 Solving -0.78125 + t = -0.89322537 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -0.89322537 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -0.89322537 + 0.78125 t = -0.89322537 + 0.78125 Combine like terms: -0.89322537 + 0.78125 = -0.11197537 t = -0.11197537 Simplifying t = -0.11197537

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.67447537, -0.11197537}

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