16t^2-20t-25=0

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Solution for 16t^2-20t-25=0 equation:


Simplifying
16t2 + -20t + -25 = 0

Reorder the terms:
-25 + -20t + 16t2 = 0

Solving
-25 + -20t + 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'.
-1.5625 + -1.25t + t2 = 0

Move the constant term to the right:

Add '1.5625' to each side of the equation.
-1.5625 + -1.25t + 1.5625 + t2 = 0 + 1.5625

Reorder the terms:
-1.5625 + 1.5625 + -1.25t + t2 = 0 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + -1.25t + t2 = 0 + 1.5625
-1.25t + t2 = 0 + 1.5625

Combine like terms: 0 + 1.5625 = 1.5625
-1.25t + t2 = 1.5625

The t term is -1.25t.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25t + 0.390625 + t2 = 1.5625 + 0.390625

Reorder the terms:
0.390625 + -1.25t + t2 = 1.5625 + 0.390625

Combine like terms: 1.5625 + 0.390625 = 1.953125
0.390625 + -1.25t + t2 = 1.953125

Factor a perfect square on the left side:
(t + -0.625)(t + -0.625) = 1.953125

Calculate the square root of the right side: 1.397542486

Break this problem into two subproblems by setting 
(t + -0.625) equal to 1.397542486 and -1.397542486.

Subproblem 1

t + -0.625 = 1.397542486 Simplifying t + -0.625 = 1.397542486 Reorder the terms: -0.625 + t = 1.397542486 Solving -0.625 + t = 1.397542486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 1.397542486 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 1.397542486 + 0.625 t = 1.397542486 + 0.625 Combine like terms: 1.397542486 + 0.625 = 2.022542486 t = 2.022542486 Simplifying t = 2.022542486

Subproblem 2

t + -0.625 = -1.397542486 Simplifying t + -0.625 = -1.397542486 Reorder the terms: -0.625 + t = -1.397542486 Solving -0.625 + t = -1.397542486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -1.397542486 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -1.397542486 + 0.625 t = -1.397542486 + 0.625 Combine like terms: -1.397542486 + 0.625 = -0.772542486 t = -0.772542486 Simplifying t = -0.772542486

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.022542486, -0.772542486}

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