16t^2-17t+4=0

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Solution for 16t^2-17t+4=0 equation:


Simplifying
16t2 + -17t + 4 = 0

Reorder the terms:
4 + -17t + 16t2 = 0

Solving
4 + -17t + 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'.
0.25 + -1.0625t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.0625t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.0625t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.0625t + t2 = 0 + -0.25
-1.0625t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.0625t + t2 = -0.25

The t term is -1.0625t.  Take half its coefficient (-0.53125).
Square it (0.2822265625) and add it to both sides.

Add '0.2822265625' to each side of the equation.
-1.0625t + 0.2822265625 + t2 = -0.25 + 0.2822265625

Reorder the terms:
0.2822265625 + -1.0625t + t2 = -0.25 + 0.2822265625

Combine like terms: -0.25 + 0.2822265625 = 0.0322265625
0.2822265625 + -1.0625t + t2 = 0.0322265625

Factor a perfect square on the left side:
(t + -0.53125)(t + -0.53125) = 0.0322265625

Calculate the square root of the right side: 0.179517583

Break this problem into two subproblems by setting 
(t + -0.53125) equal to 0.179517583 and -0.179517583.

Subproblem 1

t + -0.53125 = 0.179517583 Simplifying t + -0.53125 = 0.179517583 Reorder the terms: -0.53125 + t = 0.179517583 Solving -0.53125 + t = 0.179517583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = 0.179517583 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = 0.179517583 + 0.53125 t = 0.179517583 + 0.53125 Combine like terms: 0.179517583 + 0.53125 = 0.710767583 t = 0.710767583 Simplifying t = 0.710767583

Subproblem 2

t + -0.53125 = -0.179517583 Simplifying t + -0.53125 = -0.179517583 Reorder the terms: -0.53125 + t = -0.179517583 Solving -0.53125 + t = -0.179517583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = -0.179517583 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = -0.179517583 + 0.53125 t = -0.179517583 + 0.53125 Combine like terms: -0.179517583 + 0.53125 = 0.351732417 t = 0.351732417 Simplifying t = 0.351732417

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.710767583, 0.351732417}

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