16t^2-113t+39=0

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Solution for 16t^2-113t+39=0 equation:


Simplifying
16t2 + -113t + 39 = 0

Reorder the terms:
39 + -113t + 16t2 = 0

Solving
39 + -113t + 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'.
2.4375 + -7.0625t + t2 = 0

Move the constant term to the right:

Add '-2.4375' to each side of the equation.
2.4375 + -7.0625t + -2.4375 + t2 = 0 + -2.4375

Reorder the terms:
2.4375 + -2.4375 + -7.0625t + t2 = 0 + -2.4375

Combine like terms: 2.4375 + -2.4375 = 0.0000
0.0000 + -7.0625t + t2 = 0 + -2.4375
-7.0625t + t2 = 0 + -2.4375

Combine like terms: 0 + -2.4375 = -2.4375
-7.0625t + t2 = -2.4375

The t term is -7.0625t.  Take half its coefficient (-3.53125).
Square it (12.46972656) and add it to both sides.

Add '12.46972656' to each side of the equation.
-7.0625t + 12.46972656 + t2 = -2.4375 + 12.46972656

Reorder the terms:
12.46972656 + -7.0625t + t2 = -2.4375 + 12.46972656

Combine like terms: -2.4375 + 12.46972656 = 10.03222656
12.46972656 + -7.0625t + t2 = 10.03222656

Factor a perfect square on the left side:
(t + -3.53125)(t + -3.53125) = 10.03222656

Calculate the square root of the right side: 3.167369028

Break this problem into two subproblems by setting 
(t + -3.53125) equal to 3.167369028 and -3.167369028.

Subproblem 1

t + -3.53125 = 3.167369028 Simplifying t + -3.53125 = 3.167369028 Reorder the terms: -3.53125 + t = 3.167369028 Solving -3.53125 + t = 3.167369028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = 3.167369028 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = 3.167369028 + 3.53125 t = 3.167369028 + 3.53125 Combine like terms: 3.167369028 + 3.53125 = 6.698619028 t = 6.698619028 Simplifying t = 6.698619028

Subproblem 2

t + -3.53125 = -3.167369028 Simplifying t + -3.53125 = -3.167369028 Reorder the terms: -3.53125 + t = -3.167369028 Solving -3.53125 + t = -3.167369028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = -3.167369028 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = -3.167369028 + 3.53125 t = -3.167369028 + 3.53125 Combine like terms: -3.167369028 + 3.53125 = 0.363880972 t = 0.363880972 Simplifying t = 0.363880972

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.698619028, 0.363880972}

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