0=16t^2-14t+2.75

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Solution for 0=16t^2-14t+2.75 equation:


Simplifying
0 = 16t2 + -14t + 2.75

Reorder the terms:
0 = 2.75 + -14t + 16t2

Solving
0 = 2.75 + -14t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -2.75 = -2.75
-2.75 + 14t + -16t2 = 2.75 + -14t + 16t2 + -2.75 + 14t + -16t2

Reorder the terms:
-2.75 + 14t + -16t2 = 2.75 + -2.75 + -14t + 14t + 16t2 + -16t2

Combine like terms: 2.75 + -2.75 = 0.00
-2.75 + 14t + -16t2 = 0.00 + -14t + 14t + 16t2 + -16t2
-2.75 + 14t + -16t2 = -14t + 14t + 16t2 + -16t2

Combine like terms: -14t + 14t = 0
-2.75 + 14t + -16t2 = 0 + 16t2 + -16t2
-2.75 + 14t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-2.75 + 14t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.171875 + -0.875t + t2 = 0

Move the constant term to the right:

Add '-0.171875' to each side of the equation.
0.171875 + -0.875t + -0.171875 + t2 = 0 + -0.171875

Reorder the terms:
0.171875 + -0.171875 + -0.875t + t2 = 0 + -0.171875

Combine like terms: 0.171875 + -0.171875 = 0.000000
0.000000 + -0.875t + t2 = 0 + -0.171875
-0.875t + t2 = 0 + -0.171875

Combine like terms: 0 + -0.171875 = -0.171875
-0.875t + t2 = -0.171875

The t term is -0.875t.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875t + 0.19140625 + t2 = -0.171875 + 0.19140625

Reorder the terms:
0.19140625 + -0.875t + t2 = -0.171875 + 0.19140625

Combine like terms: -0.171875 + 0.19140625 = 0.01953125
0.19140625 + -0.875t + t2 = 0.01953125

Factor a perfect square on the left side:
(t + -0.4375)(t + -0.4375) = 0.01953125

Calculate the square root of the right side: 0.139754249

Break this problem into two subproblems by setting 
(t + -0.4375) equal to 0.139754249 and -0.139754249.

Subproblem 1

t + -0.4375 = 0.139754249 Simplifying t + -0.4375 = 0.139754249 Reorder the terms: -0.4375 + t = 0.139754249 Solving -0.4375 + t = 0.139754249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = 0.139754249 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = 0.139754249 + 0.4375 t = 0.139754249 + 0.4375 Combine like terms: 0.139754249 + 0.4375 = 0.577254249 t = 0.577254249 Simplifying t = 0.577254249

Subproblem 2

t + -0.4375 = -0.139754249 Simplifying t + -0.4375 = -0.139754249 Reorder the terms: -0.4375 + t = -0.139754249 Solving -0.4375 + t = -0.139754249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = -0.139754249 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = -0.139754249 + 0.4375 t = -0.139754249 + 0.4375 Combine like terms: -0.139754249 + 0.4375 = 0.297745751 t = 0.297745751 Simplifying t = 0.297745751

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.577254249, 0.297745751}

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