15b^2-32b+14=0

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Solution for 15b^2-32b+14=0 equation: 


Simplifying
15b2 + -32b + 14 = 0

Reorder the terms:
14 + -32b + 15b2 = 0

Solving
14 + -32b + 15b2 = 0

Solving for variable 'b'.

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

Divide each side by '15'.
0.9333333333 + -2.133333333b + b2 = 0

Move the constant term to the right:

Add '-0.9333333333' to each side of the equation.
0.9333333333 + -2.133333333b + -0.9333333333 + b2 = 0 + -0.9333333333

Reorder the terms:
0.9333333333 + -0.9333333333 + -2.133333333b + b2 = 0 + -0.9333333333

Combine like terms: 0.9333333333 + -0.9333333333 = 0.0000000000
0.0000000000 + -2.133333333b + b2 = 0 + -0.9333333333
-2.133333333b + b2 = 0 + -0.9333333333

Combine like terms: 0 + -0.9333333333 = -0.9333333333
-2.133333333b + b2 = -0.9333333333

The b term is -2.133333333b.  Take half its coefficient (-1.066666667).
Square it (1.137777778) and add it to both sides.

Add '1.137777778' to each side of the equation.
-2.133333333b + 1.137777778 + b2 = -0.9333333333 + 1.137777778

Reorder the terms:
1.137777778 + -2.133333333b + b2 = -0.9333333333 + 1.137777778

Combine like terms: -0.9333333333 + 1.137777778 = 0.2044444447
1.137777778 + -2.133333333b + b2 = 0.2044444447

Factor a perfect square on the left side:
(b + -1.066666667)(b + -1.066666667) = 0.2044444447

Calculate the square root of the right side: 0.452155332

Break this problem into two subproblems by setting 
(b + -1.066666667) equal to 0.452155332 and -0.452155332.


Subproblem 1
b + -1.066666667 = 0.452155332

Simplifying
b + -1.066666667 = 0.452155332

Reorder the terms:
-1.066666667 + b = 0.452155332

Solving
-1.066666667 + b = 0.452155332

Solving for variable 'b'.

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

Add '1.066666667' to each side of the equation.
-1.066666667 + 1.066666667 + b = 0.452155332 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + b = 0.452155332 + 1.066666667
b = 0.452155332 + 1.066666667

Combine like terms: 0.452155332 + 1.066666667 = 1.518821999
b = 1.518821999

Simplifying
b = 1.518821999


Subproblem 2
b + -1.066666667 = -0.452155332

Simplifying
b + -1.066666667 = -0.452155332

Reorder the terms:
-1.066666667 + b = -0.452155332

Solving
-1.066666667 + b = -0.452155332

Solving for variable 'b'.

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

Add '1.066666667' to each side of the equation.
-1.066666667 + 1.066666667 + b = -0.452155332 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + b = -0.452155332 + 1.066666667
b = -0.452155332 + 1.066666667

Combine like terms: -0.452155332 + 1.066666667 = 0.614511335
b = 0.614511335

Simplifying
b = 0.614511335


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.518821999, 0.614511335}

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