b^2+3b-96.89=9.60

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Solution for b^2+3b-96.89=9.60 equation: 


Simplifying
b2 + 3b + -96.89 = 9.60

Reorder the terms:
-96.89 + 3b + b2 = 9.60

Solving
-96.89 + 3b + b2 = 9.60

Solving for variable 'b'.

Reorder the terms:
-96.89 + -9.60 + 3b + b2 = 9.60 + -9.60

Combine like terms: -96.89 + -9.60 = -106.49
-106.49 + 3b + b2 = 9.60 + -9.60

Combine like terms: 9.60 + -9.60 = 0.00
-106.49 + 3b + b2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '106.49' to each side of the equation.
-106.49 + 3b + 106.49 + b2 = 0.00 + 106.49

Reorder the terms:
-106.49 + 106.49 + 3b + b2 = 0.00 + 106.49

Combine like terms: -106.49 + 106.49 = 0.00
0.00 + 3b + b2 = 0.00 + 106.49
3b + b2 = 0.00 + 106.49

Combine like terms: 0.00 + 106.49 = 106.49
3b + b2 = 106.49

The b term is 3b.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3b + 2.25 + b2 = 106.49 + 2.25

Reorder the terms:
2.25 + 3b + b2 = 106.49 + 2.25

Combine like terms: 106.49 + 2.25 = 108.74
2.25 + 3b + b2 = 108.74

Factor a perfect square on the left side:
(b + 1.5)(b + 1.5) = 108.74

Calculate the square root of the right side: 10.427847333

Break this problem into two subproblems by setting 
(b + 1.5) equal to 10.427847333 and -10.427847333.


Subproblem 1
b + 1.5 = 10.427847333

Simplifying
b + 1.5 = 10.427847333

Reorder the terms:
1.5 + b = 10.427847333

Solving
1.5 + b = 10.427847333

Solving for variable 'b'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + b = 10.427847333 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = 10.427847333 + -1.5
b = 10.427847333 + -1.5

Combine like terms: 10.427847333 + -1.5 = 8.927847333
b = 8.927847333

Simplifying
b = 8.927847333


Subproblem 2
b + 1.5 = -10.427847333

Simplifying
b + 1.5 = -10.427847333

Reorder the terms:
1.5 + b = -10.427847333

Solving
1.5 + b = -10.427847333

Solving for variable 'b'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + b = -10.427847333 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = -10.427847333 + -1.5
b = -10.427847333 + -1.5

Combine like terms: -10.427847333 + -1.5 = -11.927847333
b = -11.927847333

Simplifying
b = -11.927847333


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {8.927847333, -11.927847333}

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