5b^2+4b=3

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Solution for 5b^2+4b=3 equation:


Simplifying
5b2 + 4b = 3

Reorder the terms:
4b + 5b2 = 3

Solving
4b + 5b2 = 3

Solving for variable 'b'.

Reorder the terms:
-3 + 4b + 5b2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 4b + 5b2 = 0

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

Divide each side by '5'.
-0.6 + 0.8b + b2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.8b + 0.6 + b2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.8b + b2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.8b + b2 = 0 + 0.6
0.8b + b2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.8b + b2 = 0.6

The b term is 0.8b.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8b + 0.16 + b2 = 0.6 + 0.16

Reorder the terms:
0.16 + 0.8b + b2 = 0.6 + 0.16

Combine like terms: 0.6 + 0.16 = 0.76
0.16 + 0.8b + b2 = 0.76

Factor a perfect square on the left side:
(b + 0.4)(b + 0.4) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(b + 0.4) equal to 0.871779789 and -0.871779789.

Subproblem 1

b + 0.4 = 0.871779789 Simplifying b + 0.4 = 0.871779789 Reorder the terms: 0.4 + b = 0.871779789 Solving 0.4 + b = 0.871779789 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + b = 0.871779789 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + b = 0.871779789 + -0.4 b = 0.871779789 + -0.4 Combine like terms: 0.871779789 + -0.4 = 0.471779789 b = 0.471779789 Simplifying b = 0.471779789

Subproblem 2

b + 0.4 = -0.871779789 Simplifying b + 0.4 = -0.871779789 Reorder the terms: 0.4 + b = -0.871779789 Solving 0.4 + b = -0.871779789 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + b = -0.871779789 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + b = -0.871779789 + -0.4 b = -0.871779789 + -0.4 Combine like terms: -0.871779789 + -0.4 = -1.271779789 b = -1.271779789 Simplifying b = -1.271779789

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.471779789, -1.271779789}

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