2=8t-5t^2

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Solution for 2=8t-5t^2 equation:


Simplifying
2 = 8t + -5t2

Solving
2 = 8t + -5t2

Solving for variable 't'.

Reorder the terms:
2 + -8t + 5t2 = 8t + -8t + -5t2 + 5t2

Combine like terms: 8t + -8t = 0
2 + -8t + 5t2 = 0 + -5t2 + 5t2
2 + -8t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
2 + -8t + 5t2 = 0

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

Divide each side by '5'.
0.4 + -1.6t + t2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -1.6t + -0.4 + t2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -1.6t + t2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -1.6t + t2 = 0 + -0.4
-1.6t + t2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-1.6t + t2 = -0.4

The t term is -1.6t.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6t + 0.64 + t2 = -0.4 + 0.64

Reorder the terms:
0.64 + -1.6t + t2 = -0.4 + 0.64

Combine like terms: -0.4 + 0.64 = 0.24
0.64 + -1.6t + t2 = 0.24

Factor a perfect square on the left side:
(t + -0.8)(t + -0.8) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(t + -0.8) equal to 0.489897949 and -0.489897949.

Subproblem 1

t + -0.8 = 0.489897949 Simplifying t + -0.8 = 0.489897949 Reorder the terms: -0.8 + t = 0.489897949 Solving -0.8 + t = 0.489897949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 0.489897949 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 0.489897949 + 0.8 t = 0.489897949 + 0.8 Combine like terms: 0.489897949 + 0.8 = 1.289897949 t = 1.289897949 Simplifying t = 1.289897949

Subproblem 2

t + -0.8 = -0.489897949 Simplifying t + -0.8 = -0.489897949 Reorder the terms: -0.8 + t = -0.489897949 Solving -0.8 + t = -0.489897949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -0.489897949 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -0.489897949 + 0.8 t = -0.489897949 + 0.8 Combine like terms: -0.489897949 + 0.8 = 0.310102051 t = 0.310102051 Simplifying t = 0.310102051

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.289897949, 0.310102051}

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