3t^2+6t-11=0

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Solution for 3t^2+6t-11=0 equation:


Simplifying
3t2 + 6t + -11 = 0

Reorder the terms:
-11 + 6t + 3t2 = 0

Solving
-11 + 6t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
-3.666666667 + 2t + t2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 2t + 3.666666667 + t2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 2t + t2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 2t + t2 = 0 + 3.666666667
2t + t2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
2t + t2 = 3.666666667

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 3.666666667 + 1

Reorder the terms:
1 + 2t + t2 = 3.666666667 + 1

Combine like terms: 3.666666667 + 1 = 4.666666667
1 + 2t + t2 = 4.666666667

Factor a perfect square on the left side:
(t + 1)(t + 1) = 4.666666667

Calculate the square root of the right side: 2.1602469

Break this problem into two subproblems by setting 
(t + 1) equal to 2.1602469 and -2.1602469.

Subproblem 1

t + 1 = 2.1602469 Simplifying t + 1 = 2.1602469 Reorder the terms: 1 + t = 2.1602469 Solving 1 + t = 2.1602469 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 2.1602469 + -1 Combine like terms: 1 + -1 = 0 0 + t = 2.1602469 + -1 t = 2.1602469 + -1 Combine like terms: 2.1602469 + -1 = 1.1602469 t = 1.1602469 Simplifying t = 1.1602469

Subproblem 2

t + 1 = -2.1602469 Simplifying t + 1 = -2.1602469 Reorder the terms: 1 + t = -2.1602469 Solving 1 + t = -2.1602469 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -2.1602469 + -1 Combine like terms: 1 + -1 = 0 0 + t = -2.1602469 + -1 t = -2.1602469 + -1 Combine like terms: -2.1602469 + -1 = -3.1602469 t = -3.1602469 Simplifying t = -3.1602469

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.1602469, -3.1602469}

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