9=t^2-6t

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Solution for 9=t^2-6t equation:


Simplifying
9 = t2 + -6t

Reorder the terms:
9 = -6t + t2

Solving
9 = -6t + t2

Solving for variable 't'.

Reorder the terms:
9 + 6t + -1t2 = -6t + 6t + t2 + -1t2

Combine like terms: -6t + 6t = 0
9 + 6t + -1t2 = 0 + t2 + -1t2
9 + 6t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
9 + 6t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + -6t + t2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -6t + 9 + t2 = 0 + 9

Reorder the terms:
-9 + 9 + -6t + t2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -6t + t2 = 0 + 9
-6t + t2 = 0 + 9

Combine like terms: 0 + 9 = 9
-6t + t2 = 9

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 = 9 + 9

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

Combine like terms: 9 + 9 = 18
9 + -6t + t2 = 18

Factor a perfect square on the left side:
(t + -3)(t + -3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(t + -3) equal to 4.242640687 and -4.242640687.

Subproblem 1

t + -3 = 4.242640687 Simplifying t + -3 = 4.242640687 Reorder the terms: -3 + t = 4.242640687 Solving -3 + t = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.242640687 + 3 t = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 t = 7.242640687 Simplifying t = 7.242640687

Subproblem 2

t + -3 = -4.242640687 Simplifying t + -3 = -4.242640687 Reorder the terms: -3 + t = -4.242640687 Solving -3 + t = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.242640687 + 3 t = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 t = -1.242640687 Simplifying t = -1.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.242640687, -1.242640687}

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