5(t^2+t-9)=0

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Solution for 5(t^2+t-9)=0 equation: 


Simplifying
5(t2 + t + -9) = 0

Reorder the terms:
5(-9 + t + t2) = 0
(-9 * 5 + t * 5 + t2 * 5) = 0
(-45 + 5t + 5t2) = 0

Solving
-45 + 5t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-9 + t + t2)' equal to zero and attempt to solve:

Simplifying
-9 + t + t2 = 0

Solving
-9 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 9 + 0.25

Reorder the terms:
0.25 + t + t2 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + t + t2 = 9.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(t + 0.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
t + 0.5 = 3.041381265

Simplifying
t + 0.5 = 3.041381265

Reorder the terms:
0.5 + t = 3.041381265

Solving
0.5 + t = 3.041381265

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 3.041381265 + -0.5
t = 3.041381265 + -0.5

Combine like terms: 3.041381265 + -0.5 = 2.541381265
t = 2.541381265

Simplifying
t = 2.541381265


Subproblem 2
t + 0.5 = -3.041381265

Simplifying
t + 0.5 = -3.041381265

Reorder the terms:
0.5 + t = -3.041381265

Solving
0.5 + t = -3.041381265

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -3.041381265 + -0.5
t = -3.041381265 + -0.5

Combine like terms: -3.041381265 + -0.5 = -3.541381265
t = -3.541381265

Simplifying
t = -3.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.541381265, -3.541381265}
Solution
t = {2.541381265, -3.541381265}

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