t^2+9t+9=0

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Solution for t^2+9t+9=0 equation:


Simplifying
t2 + 9t + 9 = 0

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

Solving
9 + 9t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The t term is 9t.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9t + 20.25 + t2 = -9 + 20.25

Reorder the terms:
20.25 + 9t + t2 = -9 + 20.25

Combine like terms: -9 + 20.25 = 11.25
20.25 + 9t + t2 = 11.25

Factor a perfect square on the left side:
(t + 4.5)(t + 4.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(t + 4.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

t + 4.5 = 3.354101966 Simplifying t + 4.5 = 3.354101966 Reorder the terms: 4.5 + t = 3.354101966 Solving 4.5 + t = 3.354101966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + t = 3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + t = 3.354101966 + -4.5 t = 3.354101966 + -4.5 Combine like terms: 3.354101966 + -4.5 = -1.145898034 t = -1.145898034 Simplifying t = -1.145898034

Subproblem 2

t + 4.5 = -3.354101966 Simplifying t + 4.5 = -3.354101966 Reorder the terms: 4.5 + t = -3.354101966 Solving 4.5 + t = -3.354101966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + t = -3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + t = -3.354101966 + -4.5 t = -3.354101966 + -4.5 Combine like terms: -3.354101966 + -4.5 = -7.854101966 t = -7.854101966 Simplifying t = -7.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-1.145898034, -7.854101966}

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