2+5t-5t^2=0

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


Simplifying
2 + 5t + -5t2 = 0

Solving
2 + 5t + -5t2 = 0

Solving for variable 't'.

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

Divide each side by '-5'.
-0.4 + -1t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1t + t2 = 0 + 0.4
-1t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1t + t2 = 0.4

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 0.4 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 0.4 + 0.25

Combine like terms: 0.4 + 0.25 = 0.65
0.25 + -1t + t2 = 0.65

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.65

Calculate the square root of the right side: 0.806225775

Break this problem into two subproblems by setting 
(t + -0.5) equal to 0.806225775 and -0.806225775.

Subproblem 1

t + -0.5 = 0.806225775 Simplifying t + -0.5 = 0.806225775 Reorder the terms: -0.5 + t = 0.806225775 Solving -0.5 + t = 0.806225775 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.806225775 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.806225775 + 0.5 t = 0.806225775 + 0.5 Combine like terms: 0.806225775 + 0.5 = 1.306225775 t = 1.306225775 Simplifying t = 1.306225775

Subproblem 2

t + -0.5 = -0.806225775 Simplifying t + -0.5 = -0.806225775 Reorder the terms: -0.5 + t = -0.806225775 Solving -0.5 + t = -0.806225775 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.806225775 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.806225775 + 0.5 t = -0.806225775 + 0.5 Combine like terms: -0.806225775 + 0.5 = -0.306225775 t = -0.306225775 Simplifying t = -0.306225775

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.306225775, -0.306225775}

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