-16t^2+63t-16=0

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Solution for -16t^2+63t-16=0 equation:


Simplifying
-16t2 + 63t + -16 = 0

Reorder the terms:
-16 + 63t + -16t2 = 0

Solving
-16 + 63t + -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 + -3.9375t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.9375t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -3.9375t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.9375t + t2 = 0 + -1
-3.9375t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.9375t + t2 = -1

The t term is -3.9375t.  Take half its coefficient (-1.96875).
Square it (3.875976563) and add it to both sides.

Add '3.875976563' to each side of the equation.
-3.9375t + 3.875976563 + t2 = -1 + 3.875976563

Reorder the terms:
3.875976563 + -3.9375t + t2 = -1 + 3.875976563

Combine like terms: -1 + 3.875976563 = 2.875976563
3.875976563 + -3.9375t + t2 = 2.875976563

Factor a perfect square on the left side:
(t + -1.96875)(t + -1.96875) = 2.875976563

Calculate the square root of the right side: 1.695870444

Break this problem into two subproblems by setting 
(t + -1.96875) equal to 1.695870444 and -1.695870444.

Subproblem 1

t + -1.96875 = 1.695870444 Simplifying t + -1.96875 = 1.695870444 Reorder the terms: -1.96875 + t = 1.695870444 Solving -1.96875 + t = 1.695870444 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + t = 1.695870444 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + t = 1.695870444 + 1.96875 t = 1.695870444 + 1.96875 Combine like terms: 1.695870444 + 1.96875 = 3.664620444 t = 3.664620444 Simplifying t = 3.664620444

Subproblem 2

t + -1.96875 = -1.695870444 Simplifying t + -1.96875 = -1.695870444 Reorder the terms: -1.96875 + t = -1.695870444 Solving -1.96875 + t = -1.695870444 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + t = -1.695870444 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + t = -1.695870444 + 1.96875 t = -1.695870444 + 1.96875 Combine like terms: -1.695870444 + 1.96875 = 0.272879556 t = 0.272879556 Simplifying t = 0.272879556

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.664620444, 0.272879556}

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