-0.1t^2+2.8t+2=5

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Solution for -0.1t^2+2.8t+2=5 equation:


Simplifying
-0.1t2 + 2.8t + 2 = 5

Reorder the terms:
2 + 2.8t + -0.1t2 = 5

Solving
2 + 2.8t + -0.1t2 = 5

Solving for variable 't'.

Reorder the terms:
2 + -5 + 2.8t + -0.1t2 = 5 + -5

Combine like terms: 2 + -5 = -3
-3 + 2.8t + -0.1t2 = 5 + -5

Combine like terms: 5 + -5 = 0
-3 + 2.8t + -0.1t2 = 0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
30 + -28t + t2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -28t + -30 + t2 = 0 + -30

Reorder the terms:
30 + -30 + -28t + t2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -28t + t2 = 0 + -30
-28t + t2 = 0 + -30

Combine like terms: 0 + -30 = -30
-28t + t2 = -30

The t term is -28t.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28t + 196 + t2 = -30 + 196

Reorder the terms:
196 + -28t + t2 = -30 + 196

Combine like terms: -30 + 196 = 166
196 + -28t + t2 = 166

Factor a perfect square on the left side:
(t + -14)(t + -14) = 166

Calculate the square root of the right side: 12.884098727

Break this problem into two subproblems by setting 
(t + -14) equal to 12.884098727 and -12.884098727.

Subproblem 1

t + -14 = 12.884098727 Simplifying t + -14 = 12.884098727 Reorder the terms: -14 + t = 12.884098727 Solving -14 + t = 12.884098727 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = 12.884098727 + 14 Combine like terms: -14 + 14 = 0 0 + t = 12.884098727 + 14 t = 12.884098727 + 14 Combine like terms: 12.884098727 + 14 = 26.884098727 t = 26.884098727 Simplifying t = 26.884098727

Subproblem 2

t + -14 = -12.884098727 Simplifying t + -14 = -12.884098727 Reorder the terms: -14 + t = -12.884098727 Solving -14 + t = -12.884098727 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = -12.884098727 + 14 Combine like terms: -14 + 14 = 0 0 + t = -12.884098727 + 14 t = -12.884098727 + 14 Combine like terms: -12.884098727 + 14 = 1.115901273 t = 1.115901273 Simplifying t = 1.115901273

Solution

The solution to the problem is based on the solutions from the subproblems. t = {26.884098727, 1.115901273}

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