0=-5t^2+12t+2

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Solution for 0=-5t^2+12t+2 equation:


Simplifying
0 = -5t2 + 12t + 2

Reorder the terms:
0 = 2 + 12t + -5t2

Solving
0 = 2 + 12t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -2 = -2
-2 + -12t + 5t2 = 2 + 12t + -5t2 + -2 + -12t + 5t2

Reorder the terms:
-2 + -12t + 5t2 = 2 + -2 + 12t + -12t + -5t2 + 5t2

Combine like terms: 2 + -2 = 0
-2 + -12t + 5t2 = 0 + 12t + -12t + -5t2 + 5t2
-2 + -12t + 5t2 = 12t + -12t + -5t2 + 5t2

Combine like terms: 12t + -12t = 0
-2 + -12t + 5t2 = 0 + -5t2 + 5t2
-2 + -12t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-2 + -12t + 5t2 = 0

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

Divide each side by '5'.
-0.4 + -2.4t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -2.4t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -2.4t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -2.4t + t2 = 0 + 0.4
-2.4t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-2.4t + t2 = 0.4

The t term is -2.4t.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4t + 1.44 + t2 = 0.4 + 1.44

Reorder the terms:
1.44 + -2.4t + t2 = 0.4 + 1.44

Combine like terms: 0.4 + 1.44 = 1.84
1.44 + -2.4t + t2 = 1.84

Factor a perfect square on the left side:
(t + -1.2)(t + -1.2) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(t + -1.2) equal to 1.356465997 and -1.356465997.

Subproblem 1

t + -1.2 = 1.356465997 Simplifying t + -1.2 = 1.356465997 Reorder the terms: -1.2 + t = 1.356465997 Solving -1.2 + t = 1.356465997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 1.356465997 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 1.356465997 + 1.2 t = 1.356465997 + 1.2 Combine like terms: 1.356465997 + 1.2 = 2.556465997 t = 2.556465997 Simplifying t = 2.556465997

Subproblem 2

t + -1.2 = -1.356465997 Simplifying t + -1.2 = -1.356465997 Reorder the terms: -1.2 + t = -1.356465997 Solving -1.2 + t = -1.356465997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -1.356465997 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -1.356465997 + 1.2 t = -1.356465997 + 1.2 Combine like terms: -1.356465997 + 1.2 = -0.156465997 t = -0.156465997 Simplifying t = -0.156465997

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.556465997, -0.156465997}

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