4b*4b-8b-5=0

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Solution for 4b*4b-8b-5=0 equation:


Simplifying
4b * 4b + -8b + -5 = 0

Reorder the terms for easier multiplication:
4 * 4b * b + -8b + -5 = 0

Multiply 4 * 4
16b * b + -8b + -5 = 0

Multiply b * b
16b2 + -8b + -5 = 0

Reorder the terms:
-5 + -8b + 16b2 = 0

Solving
-5 + -8b + 16b2 = 0

Solving for variable 'b'.

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

Divide each side by '16'.
-0.3125 + -0.5b + b2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -0.5b + 0.3125 + b2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -0.5b + b2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -0.5b + b2 = 0 + 0.3125
-0.5b + b2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-0.5b + b2 = 0.3125

The b term is -0.5b.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5b + 0.0625 + b2 = 0.3125 + 0.0625

Reorder the terms:
0.0625 + -0.5b + b2 = 0.3125 + 0.0625

Combine like terms: 0.3125 + 0.0625 = 0.375
0.0625 + -0.5b + b2 = 0.375

Factor a perfect square on the left side:
(b + -0.25)(b + -0.25) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(b + -0.25) equal to 0.612372436 and -0.612372436.

Subproblem 1

b + -0.25 = 0.612372436 Simplifying b + -0.25 = 0.612372436 Reorder the terms: -0.25 + b = 0.612372436 Solving -0.25 + b = 0.612372436 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = 0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = 0.612372436 + 0.25 b = 0.612372436 + 0.25 Combine like terms: 0.612372436 + 0.25 = 0.862372436 b = 0.862372436 Simplifying b = 0.862372436

Subproblem 2

b + -0.25 = -0.612372436 Simplifying b + -0.25 = -0.612372436 Reorder the terms: -0.25 + b = -0.612372436 Solving -0.25 + b = -0.612372436 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = -0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = -0.612372436 + 0.25 b = -0.612372436 + 0.25 Combine like terms: -0.612372436 + 0.25 = -0.362372436 b = -0.362372436 Simplifying b = -0.362372436

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.862372436, -0.362372436}

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