4=40t-5t^2

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Solution for 4=40t-5t^2 equation:


Simplifying
4 = 40t + -5t2

Solving
4 = 40t + -5t2

Solving for variable 't'.

Reorder the terms:
4 + -40t + 5t2 = 40t + -40t + -5t2 + 5t2

Combine like terms: 40t + -40t = 0
4 + -40t + 5t2 = 0 + -5t2 + 5t2
4 + -40t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
4 + -40t + 5t2 = 0

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

Divide each side by '5'.
0.8 + -8t + t2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -8t + -0.8 + t2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -8t + t2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -8t + t2 = 0 + -0.8
-8t + t2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-8t + t2 = -0.8

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = -0.8 + 16

Reorder the terms:
16 + -8t + t2 = -0.8 + 16

Combine like terms: -0.8 + 16 = 15.2
16 + -8t + t2 = 15.2

Factor a perfect square on the left side:
(t + -4)(t + -4) = 15.2

Calculate the square root of the right side: 3.898717738

Break this problem into two subproblems by setting 
(t + -4) equal to 3.898717738 and -3.898717738.

Subproblem 1

t + -4 = 3.898717738 Simplifying t + -4 = 3.898717738 Reorder the terms: -4 + t = 3.898717738 Solving -4 + t = 3.898717738 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.898717738 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.898717738 + 4 t = 3.898717738 + 4 Combine like terms: 3.898717738 + 4 = 7.898717738 t = 7.898717738 Simplifying t = 7.898717738

Subproblem 2

t + -4 = -3.898717738 Simplifying t + -4 = -3.898717738 Reorder the terms: -4 + t = -3.898717738 Solving -4 + t = -3.898717738 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.898717738 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.898717738 + 4 t = -3.898717738 + 4 Combine like terms: -3.898717738 + 4 = 0.101282262 t = 0.101282262 Simplifying t = 0.101282262

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.898717738, 0.101282262}

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