0.08t^2-t+2=0

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Solution for 0.08t^2-t+2=0 equation:


Simplifying
0.08t2 + -1t + 2 = 0

Reorder the terms:
2 + -1t + 0.08t2 = 0

Solving
2 + -1t + 0.08t2 = 0

Solving for variable 't'.

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

Divide each side by '0.08'.
25 + -12.5t + t2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -12.5t + -25 + t2 = 0 + -25

Reorder the terms:
25 + -25 + -12.5t + t2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -12.5t + t2 = 0 + -25
-12.5t + t2 = 0 + -25

Combine like terms: 0 + -25 = -25
-12.5t + t2 = -25

The t term is -12.5t.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5t + 39.0625 + t2 = -25 + 39.0625

Reorder the terms:
39.0625 + -12.5t + t2 = -25 + 39.0625

Combine like terms: -25 + 39.0625 = 14.0625
39.0625 + -12.5t + t2 = 14.0625

Factor a perfect square on the left side:
(t + -6.25)(t + -6.25) = 14.0625

Calculate the square root of the right side: 3.75

Break this problem into two subproblems by setting 
(t + -6.25) equal to 3.75 and -3.75.

Subproblem 1

t + -6.25 = 3.75 Simplifying t + -6.25 = 3.75 Reorder the terms: -6.25 + t = 3.75 Solving -6.25 + t = 3.75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = 3.75 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 3.75 + 6.25 t = 3.75 + 6.25 Combine like terms: 3.75 + 6.25 = 10 t = 10 Simplifying t = 10

Subproblem 2

t + -6.25 = -3.75 Simplifying t + -6.25 = -3.75 Reorder the terms: -6.25 + t = -3.75 Solving -6.25 + t = -3.75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = -3.75 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -3.75 + 6.25 t = -3.75 + 6.25 Combine like terms: -3.75 + 6.25 = 2.5 t = 2.5 Simplifying t = 2.5

Solution

The solution to the problem is based on the solutions from the subproblems. t = {10, 2.5}

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