0=6t-(t*t)+11

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Solution for 0=6t-(t*t)+11 equation:


Simplifying
0 = 6t + -1(t * t) + 11

Multiply t * t
0 = 6t + -1(t2) + 11

Reorder the terms:
0 = 11 + 6t + -1t2

Solving
0 = 11 + 6t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -11 = -11
-11 + -6t + t2 = 11 + 6t + -1t2 + -11 + -6t + t2

Reorder the terms:
-11 + -6t + t2 = 11 + -11 + 6t + -6t + -1t2 + t2

Combine like terms: 11 + -11 = 0
-11 + -6t + t2 = 0 + 6t + -6t + -1t2 + t2
-11 + -6t + t2 = 6t + -6t + -1t2 + t2

Combine like terms: 6t + -6t = 0
-11 + -6t + t2 = 0 + -1t2 + t2
-11 + -6t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-11 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -6t + 11 + t2 = 0 + 11

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

Combine like terms: -11 + 11 = 0
0 + -6t + t2 = 0 + 11
-6t + t2 = 0 + 11

Combine like terms: 0 + 11 = 11
-6t + t2 = 11

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 = 11 + 9

Reorder the terms:
9 + -6t + t2 = 11 + 9

Combine like terms: 11 + 9 = 20
9 + -6t + t2 = 20

Factor a perfect square on the left side:
(t + -3)(t + -3) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(t + -3) equal to 4.472135955 and -4.472135955.

Subproblem 1

t + -3 = 4.472135955 Simplifying t + -3 = 4.472135955 Reorder the terms: -3 + t = 4.472135955 Solving -3 + t = 4.472135955 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 = 4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.472135955 + 3 t = 4.472135955 + 3 Combine like terms: 4.472135955 + 3 = 7.472135955 t = 7.472135955 Simplifying t = 7.472135955

Subproblem 2

t + -3 = -4.472135955 Simplifying t + -3 = -4.472135955 Reorder the terms: -3 + t = -4.472135955 Solving -3 + t = -4.472135955 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 = -4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.472135955 + 3 t = -4.472135955 + 3 Combine like terms: -4.472135955 + 3 = -1.472135955 t = -1.472135955 Simplifying t = -1.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.472135955, -1.472135955}

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