13+16t-16t^2=0

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Solution for 13+16t-16t^2=0 equation:


Simplifying
13 + 16t + -16t2 = 0

Solving
13 + 16t + -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'.
-0.8125 + -1t + t2 = 0

Move the constant term to the right:

Add '0.8125' to each side of the equation.
-0.8125 + -1t + 0.8125 + t2 = 0 + 0.8125

Reorder the terms:
-0.8125 + 0.8125 + -1t + t2 = 0 + 0.8125

Combine like terms: -0.8125 + 0.8125 = 0.0000
0.0000 + -1t + t2 = 0 + 0.8125
-1t + t2 = 0 + 0.8125

Combine like terms: 0 + 0.8125 = 0.8125
-1t + t2 = 0.8125

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 0.8125 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 0.8125 + 0.25

Combine like terms: 0.8125 + 0.25 = 1.0625
0.25 + -1t + t2 = 1.0625

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(t + -0.5) equal to 1.030776406 and -1.030776406.

Subproblem 1

t + -0.5 = 1.030776406 Simplifying t + -0.5 = 1.030776406 Reorder the terms: -0.5 + t = 1.030776406 Solving -0.5 + t = 1.030776406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 1.030776406 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 1.030776406 + 0.5 t = 1.030776406 + 0.5 Combine like terms: 1.030776406 + 0.5 = 1.530776406 t = 1.530776406 Simplifying t = 1.530776406

Subproblem 2

t + -0.5 = -1.030776406 Simplifying t + -0.5 = -1.030776406 Reorder the terms: -0.5 + t = -1.030776406 Solving -0.5 + t = -1.030776406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -1.030776406 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -1.030776406 + 0.5 t = -1.030776406 + 0.5 Combine like terms: -1.030776406 + 0.5 = -0.530776406 t = -0.530776406 Simplifying t = -0.530776406

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.530776406, -0.530776406}

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