30b^2+75b+46=0

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Solution for 30b^2+75b+46=0 equation:


Simplifying
30b2 + 75b + 46 = 0

Reorder the terms:
46 + 75b + 30b2 = 0

Solving
46 + 75b + 30b2 = 0

Solving for variable 'b'.

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

Divide each side by '30'.
1.533333333 + 2.5b + b2 = 0

Move the constant term to the right:

Add '-1.533333333' to each side of the equation.
1.533333333 + 2.5b + -1.533333333 + b2 = 0 + -1.533333333

Reorder the terms:
1.533333333 + -1.533333333 + 2.5b + b2 = 0 + -1.533333333

Combine like terms: 1.533333333 + -1.533333333 = 0.000000000
0.000000000 + 2.5b + b2 = 0 + -1.533333333
2.5b + b2 = 0 + -1.533333333

Combine like terms: 0 + -1.533333333 = -1.533333333
2.5b + b2 = -1.533333333

The b term is 2.5b.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5b + 1.5625 + b2 = -1.533333333 + 1.5625

Reorder the terms:
1.5625 + 2.5b + b2 = -1.533333333 + 1.5625

Combine like terms: -1.533333333 + 1.5625 = 0.029166667
1.5625 + 2.5b + b2 = 0.029166667

Factor a perfect square on the left side:
(b + 1.25)(b + 1.25) = 0.029166667

Calculate the square root of the right side: 0.170782514

Break this problem into two subproblems by setting 
(b + 1.25) equal to 0.170782514 and -0.170782514.

Subproblem 1

b + 1.25 = 0.170782514 Simplifying b + 1.25 = 0.170782514 Reorder the terms: 1.25 + b = 0.170782514 Solving 1.25 + b = 0.170782514 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = 0.170782514 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = 0.170782514 + -1.25 b = 0.170782514 + -1.25 Combine like terms: 0.170782514 + -1.25 = -1.079217486 b = -1.079217486 Simplifying b = -1.079217486

Subproblem 2

b + 1.25 = -0.170782514 Simplifying b + 1.25 = -0.170782514 Reorder the terms: 1.25 + b = -0.170782514 Solving 1.25 + b = -0.170782514 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = -0.170782514 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = -0.170782514 + -1.25 b = -0.170782514 + -1.25 Combine like terms: -0.170782514 + -1.25 = -1.420782514 b = -1.420782514 Simplifying b = -1.420782514

Solution

The solution to the problem is based on the solutions from the subproblems. b = {-1.079217486, -1.420782514}

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