t^2+6t=9

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


Simplifying
t2 + 6t = 9

Reorder the terms:
6t + t2 = 9

Solving
6t + t2 = 9

Solving for variable 't'.

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

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

Begin completing the square.

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 = 1.242640687 t = 1.242640687 Simplifying t = 1.242640687

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 = -7.242640687 t = -7.242640687 Simplifying t = -7.242640687

Solution

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

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