-16t^2+69t+3=0

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Solution for -16t^2+69t+3=0 equation:


Simplifying
-16t2 + 69t + 3 = 0

Reorder the terms:
3 + 69t + -16t2 = 0

Solving
3 + 69t + -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 + -4.3125t + t2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -4.3125t + 0.1875 + t2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -4.3125t + t2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -4.3125t + t2 = 0 + 0.1875
-4.3125t + t2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-4.3125t + t2 = 0.1875

The t term is -4.3125t.  Take half its coefficient (-2.15625).
Square it (4.649414063) and add it to both sides.

Add '4.649414063' to each side of the equation.
-4.3125t + 4.649414063 + t2 = 0.1875 + 4.649414063

Reorder the terms:
4.649414063 + -4.3125t + t2 = 0.1875 + 4.649414063

Combine like terms: 0.1875 + 4.649414063 = 4.836914063
4.649414063 + -4.3125t + t2 = 4.836914063

Factor a perfect square on the left side:
(t + -2.15625)(t + -2.15625) = 4.836914063

Calculate the square root of the right side: 2.199298539

Break this problem into two subproblems by setting 
(t + -2.15625) equal to 2.199298539 and -2.199298539.

Subproblem 1

t + -2.15625 = 2.199298539 Simplifying t + -2.15625 = 2.199298539 Reorder the terms: -2.15625 + t = 2.199298539 Solving -2.15625 + t = 2.199298539 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + t = 2.199298539 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + t = 2.199298539 + 2.15625 t = 2.199298539 + 2.15625 Combine like terms: 2.199298539 + 2.15625 = 4.355548539 t = 4.355548539 Simplifying t = 4.355548539

Subproblem 2

t + -2.15625 = -2.199298539 Simplifying t + -2.15625 = -2.199298539 Reorder the terms: -2.15625 + t = -2.199298539 Solving -2.15625 + t = -2.199298539 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + t = -2.199298539 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + t = -2.199298539 + 2.15625 t = -2.199298539 + 2.15625 Combine like terms: -2.199298539 + 2.15625 = -0.043048539 t = -0.043048539 Simplifying t = -0.043048539

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.355548539, -0.043048539}

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