0=-4t^2+16t+5

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Solution for 0=-4t^2+16t+5 equation:


Simplifying
0 = -4t2 + 16t + 5

Reorder the terms:
0 = 5 + 16t + -4t2

Solving
0 = 5 + 16t + -4t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -16t + 4t2 = 5 + 16t + -4t2 + -5 + -16t + 4t2

Reorder the terms:
-5 + -16t + 4t2 = 5 + -5 + 16t + -16t + -4t2 + 4t2

Combine like terms: 5 + -5 = 0
-5 + -16t + 4t2 = 0 + 16t + -16t + -4t2 + 4t2
-5 + -16t + 4t2 = 16t + -16t + -4t2 + 4t2

Combine like terms: 16t + -16t = 0
-5 + -16t + 4t2 = 0 + -4t2 + 4t2
-5 + -16t + 4t2 = -4t2 + 4t2

Combine like terms: -4t2 + 4t2 = 0
-5 + -16t + 4t2 = 0

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

Divide each side by '4'.
-1.25 + -4t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -4t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -4t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -4t + t2 = 0 + 1.25
-4t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-4t + t2 = 1.25

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 1.25 + 4

Reorder the terms:
4 + -4t + t2 = 1.25 + 4

Combine like terms: 1.25 + 4 = 5.25
4 + -4t + t2 = 5.25

Factor a perfect square on the left side:
(t + -2)(t + -2) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(t + -2) equal to 2.291287847 and -2.291287847.

Subproblem 1

t + -2 = 2.291287847 Simplifying t + -2 = 2.291287847 Reorder the terms: -2 + t = 2.291287847 Solving -2 + t = 2.291287847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.291287847 + 2 t = 2.291287847 + 2 Combine like terms: 2.291287847 + 2 = 4.291287847 t = 4.291287847 Simplifying t = 4.291287847

Subproblem 2

t + -2 = -2.291287847 Simplifying t + -2 = -2.291287847 Reorder the terms: -2 + t = -2.291287847 Solving -2 + t = -2.291287847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.291287847 + 2 t = -2.291287847 + 2 Combine like terms: -2.291287847 + 2 = -0.291287847 t = -0.291287847 Simplifying t = -0.291287847

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.291287847, -0.291287847}

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