7.36=t*(t+2.75)

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Solution for 7.36=t*(t+2.75) equation: 


Simplifying
7.36 = t(t + 2.75)

Reorder the terms:
7.36 = t(2.75 + t)
7.36 = (2.75 * t + t * t)
7.36 = (2.75t + t2)

Solving
7.36 = 2.75t + t2

Solving for variable 't'.

Reorder the terms:
7.36 + -2.75t + -1t2 = 2.75t + -2.75t + t2 + -1t2

Combine like terms: 2.75t + -2.75t = 0.00
7.36 + -2.75t + -1t2 = 0.00 + t2 + -1t2
7.36 + -2.75t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
7.36 + -2.75t + -1t2 = 0

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

Divide each side by '-1'.
-7.36 + 2.75t + t2 = 0

Move the constant term to the right:

Add '7.36' to each side of the equation.
-7.36 + 2.75t + 7.36 + t2 = 0 + 7.36

Reorder the terms:
-7.36 + 7.36 + 2.75t + t2 = 0 + 7.36

Combine like terms: -7.36 + 7.36 = 0.00
0.00 + 2.75t + t2 = 0 + 7.36
2.75t + t2 = 0 + 7.36

Combine like terms: 0 + 7.36 = 7.36
2.75t + t2 = 7.36

The t term is 2.75t.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75t + 1.890625 + t2 = 7.36 + 1.890625

Reorder the terms:
1.890625 + 2.75t + t2 = 7.36 + 1.890625

Combine like terms: 7.36 + 1.890625 = 9.250625
1.890625 + 2.75t + t2 = 9.250625

Factor a perfect square on the left side:
(t + 1.375)(t + 1.375) = 9.250625

Calculate the square root of the right side: 3.041484013

Break this problem into two subproblems by setting 
(t + 1.375) equal to 3.041484013 and -3.041484013.


Subproblem 1
t + 1.375 = 3.041484013

Simplifying
t + 1.375 = 3.041484013

Reorder the terms:
1.375 + t = 3.041484013

Solving
1.375 + t = 3.041484013

Solving for variable 't'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + t = 3.041484013 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + t = 3.041484013 + -1.375
t = 3.041484013 + -1.375

Combine like terms: 3.041484013 + -1.375 = 1.666484013
t = 1.666484013

Simplifying
t = 1.666484013


Subproblem 2
t + 1.375 = -3.041484013

Simplifying
t + 1.375 = -3.041484013

Reorder the terms:
1.375 + t = -3.041484013

Solving
1.375 + t = -3.041484013

Solving for variable 't'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + t = -3.041484013 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + t = -3.041484013 + -1.375
t = -3.041484013 + -1.375

Combine like terms: -3.041484013 + -1.375 = -4.416484013
t = -4.416484013

Simplifying
t = -4.416484013


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.666484013, -4.416484013}

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