2((t^2)+10t-48)=0

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Solution for 2((t^2)+10t-48)=0 equation: 


Simplifying
2((t2) + 10t + -48) = 0
2(t2 + 10t + -48) = 0

Reorder the terms:
2(-48 + 10t + t2) = 0
(-48 * 2 + 10t * 2 + t2 * 2) = 0
(-96 + 20t + 2t2) = 0

Solving
-96 + 20t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 10t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-48 + 10t + t2)' equal to zero and attempt to solve:

Simplifying
-48 + 10t + t2 = 0

Solving
-48 + 10t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 10t + 48 + t2 = 0 + 48

Reorder the terms:
-48 + 48 + 10t + t2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 10t + t2 = 0 + 48
10t + t2 = 0 + 48

Combine like terms: 0 + 48 = 48
10t + t2 = 48

The t term is 10t.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10t + 25 + t2 = 48 + 25

Reorder the terms:
25 + 10t + t2 = 48 + 25

Combine like terms: 48 + 25 = 73
25 + 10t + t2 = 73

Factor a perfect square on the left side:
(t + 5)(t + 5) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(t + 5) equal to 8.544003745 and -8.544003745.


Subproblem 1
t + 5 = 8.544003745

Simplifying
t + 5 = 8.544003745

Reorder the terms:
5 + t = 8.544003745

Solving
5 + t = 8.544003745

Solving for variable 't'.

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

Add '-5' to each side of the equation.
5 + -5 + t = 8.544003745 + -5

Combine like terms: 5 + -5 = 0
0 + t = 8.544003745 + -5
t = 8.544003745 + -5

Combine like terms: 8.544003745 + -5 = 3.544003745
t = 3.544003745

Simplifying
t = 3.544003745


Subproblem 2
t + 5 = -8.544003745

Simplifying
t + 5 = -8.544003745

Reorder the terms:
5 + t = -8.544003745

Solving
5 + t = -8.544003745

Solving for variable 't'.

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

Add '-5' to each side of the equation.
5 + -5 + t = -8.544003745 + -5

Combine like terms: 5 + -5 = 0
0 + t = -8.544003745 + -5
t = -8.544003745 + -5

Combine like terms: -8.544003745 + -5 = -13.544003745
t = -13.544003745

Simplifying
t = -13.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.544003745, -13.544003745}
Solution
t = {3.544003745, -13.544003745}

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