-6b^2+25b+11=0

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Solution for -6b^2+25b+11=0 equation: 


Simplifying
-6b2 + 25b + 11 = 0

Reorder the terms:
11 + 25b + -6b2 = 0

Solving
11 + 25b + -6b2 = 0

Solving for variable 'b'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.833333333 + -4.166666667b + b2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -4.166666667b + 1.833333333 + b2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -4.166666667b + b2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -4.166666667b + b2 = 0 + 1.833333333
-4.166666667b + b2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-4.166666667b + b2 = 1.833333333

The b term is -4.166666667b.  Take half its coefficient (-2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
-4.166666667b + 4.340277781 + b2 = 1.833333333 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667b + b2 = 1.833333333 + 4.340277781

Combine like terms: 1.833333333 + 4.340277781 = 6.173611114
4.340277781 + -4.166666667b + b2 = 6.173611114

Factor a perfect square on the left side:
(b + -2.083333334)(b + -2.083333334) = 6.173611114

Calculate the square root of the right side: 2.484675253

Break this problem into two subproblems by setting 
(b + -2.083333334) equal to 2.484675253 and -2.484675253.


Subproblem 1
b + -2.083333334 = 2.484675253

Simplifying
b + -2.083333334 = 2.484675253

Reorder the terms:
-2.083333334 + b = 2.484675253

Solving
-2.083333334 + b = 2.484675253

Solving for variable 'b'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + b = 2.484675253 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + b = 2.484675253 + 2.083333334
b = 2.484675253 + 2.083333334

Combine like terms: 2.484675253 + 2.083333334 = 4.568008587
b = 4.568008587

Simplifying
b = 4.568008587


Subproblem 2
b + -2.083333334 = -2.484675253

Simplifying
b + -2.083333334 = -2.484675253

Reorder the terms:
-2.083333334 + b = -2.484675253

Solving
-2.083333334 + b = -2.484675253

Solving for variable 'b'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + b = -2.484675253 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + b = -2.484675253 + 2.083333334
b = -2.484675253 + 2.083333334

Combine like terms: -2.484675253 + 2.083333334 = -0.401341919
b = -0.401341919

Simplifying
b = -0.401341919


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.568008587, -0.401341919}

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