2t^2+12t-5=0

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


Simplifying
2t2 + 12t + -5 = 0

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

Solving
-5 + 12t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
-2.5 + 6t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 6t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 6t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 6t + t2 = 0 + 2.5
6t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
6t + t2 = 2.5

The t term is 6t.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6t + 9 + t2 = 2.5 + 9

Reorder the terms:
9 + 6t + t2 = 2.5 + 9

Combine like terms: 2.5 + 9 = 11.5
9 + 6t + t2 = 11.5

Factor a perfect square on the left side:
(t + 3)(t + 3) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(t + 3) equal to 3.391164992 and -3.391164992.

Subproblem 1

t + 3 = 3.391164992 Simplifying t + 3 = 3.391164992 Reorder the terms: 3 + t = 3.391164992 Solving 3 + t = 3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 3.391164992 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.391164992 + -3 t = 3.391164992 + -3 Combine like terms: 3.391164992 + -3 = 0.391164992 t = 0.391164992 Simplifying t = 0.391164992

Subproblem 2

t + 3 = -3.391164992 Simplifying t + 3 = -3.391164992 Reorder the terms: 3 + t = -3.391164992 Solving 3 + t = -3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -3.391164992 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.391164992 + -3 t = -3.391164992 + -3 Combine like terms: -3.391164992 + -3 = -6.391164992 t = -6.391164992 Simplifying t = -6.391164992

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.391164992, -6.391164992}

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