-16t^2-10t+3=0

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Solution for -16t^2-10t+3=0 equation:


Simplifying
-16t2 + -10t + 3 = 0

Reorder the terms:
3 + -10t + -16t2 = 0

Solving
3 + -10t + -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 + 0.625t + t2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + 0.625t + 0.1875 + t2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + 0.625t + t2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + 0.625t + t2 = 0 + 0.1875
0.625t + t2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
0.625t + t2 = 0.1875

The t term is 0.625t.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625t + 0.09765625 + t2 = 0.1875 + 0.09765625

Reorder the terms:
0.09765625 + 0.625t + t2 = 0.1875 + 0.09765625

Combine like terms: 0.1875 + 0.09765625 = 0.28515625
0.09765625 + 0.625t + t2 = 0.28515625

Factor a perfect square on the left side:
(t + 0.3125)(t + 0.3125) = 0.28515625

Calculate the square root of the right side: 0.534000234

Break this problem into two subproblems by setting 
(t + 0.3125) equal to 0.534000234 and -0.534000234.

Subproblem 1

t + 0.3125 = 0.534000234 Simplifying t + 0.3125 = 0.534000234 Reorder the terms: 0.3125 + t = 0.534000234 Solving 0.3125 + t = 0.534000234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 0.534000234 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 0.534000234 + -0.3125 t = 0.534000234 + -0.3125 Combine like terms: 0.534000234 + -0.3125 = 0.221500234 t = 0.221500234 Simplifying t = 0.221500234

Subproblem 2

t + 0.3125 = -0.534000234 Simplifying t + 0.3125 = -0.534000234 Reorder the terms: 0.3125 + t = -0.534000234 Solving 0.3125 + t = -0.534000234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -0.534000234 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -0.534000234 + -0.3125 t = -0.534000234 + -0.3125 Combine like terms: -0.534000234 + -0.3125 = -0.846500234 t = -0.846500234 Simplifying t = -0.846500234

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.221500234, -0.846500234}

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