-21b-b(-47b)=16

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Solution for -21b-b(-47b)=16 equation:


Simplifying
-21b + -1b(-47b) = 16

Remove parenthesis around (-47b)
-21b + -1b * -47b = 16

Reorder the terms for easier multiplication:
-21b + -1 * -47b * b = 16

Multiply -1 * -47
-21b + 47b * b = 16

Multiply b * b
-21b + 47b2 = 16

Solving
-21b + 47b2 = 16

Solving for variable 'b'.

Reorder the terms:
-16 + -21b + 47b2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -21b + 47b2 = 0

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

Divide each side by '47'.
-0.3404255319 + -0.4468085106b + b2 = 0

Move the constant term to the right:

Add '0.3404255319' to each side of the equation.
-0.3404255319 + -0.4468085106b + 0.3404255319 + b2 = 0 + 0.3404255319

Reorder the terms:
-0.3404255319 + 0.3404255319 + -0.4468085106b + b2 = 0 + 0.3404255319

Combine like terms: -0.3404255319 + 0.3404255319 = 0.0000000000
0.0000000000 + -0.4468085106b + b2 = 0 + 0.3404255319
-0.4468085106b + b2 = 0 + 0.3404255319

Combine like terms: 0 + 0.3404255319 = 0.3404255319
-0.4468085106b + b2 = 0.3404255319

The b term is -0.4468085106b.  Take half its coefficient (-0.2234042553).
Square it (0.04990946129) and add it to both sides.

Add '0.04990946129' to each side of the equation.
-0.4468085106b + 0.04990946129 + b2 = 0.3404255319 + 0.04990946129

Reorder the terms:
0.04990946129 + -0.4468085106b + b2 = 0.3404255319 + 0.04990946129

Combine like terms: 0.3404255319 + 0.04990946129 = 0.39033499319
0.04990946129 + -0.4468085106b + b2 = 0.39033499319

Factor a perfect square on the left side:
(b + -0.2234042553)(b + -0.2234042553) = 0.39033499319

Calculate the square root of the right side: 0.624767951

Break this problem into two subproblems by setting 
(b + -0.2234042553) equal to 0.624767951 and -0.624767951.

Subproblem 1

b + -0.2234042553 = 0.624767951 Simplifying b + -0.2234042553 = 0.624767951 Reorder the terms: -0.2234042553 + b = 0.624767951 Solving -0.2234042553 + b = 0.624767951 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2234042553' to each side of the equation. -0.2234042553 + 0.2234042553 + b = 0.624767951 + 0.2234042553 Combine like terms: -0.2234042553 + 0.2234042553 = 0.0000000000 0.0000000000 + b = 0.624767951 + 0.2234042553 b = 0.624767951 + 0.2234042553 Combine like terms: 0.624767951 + 0.2234042553 = 0.8481722063 b = 0.8481722063 Simplifying b = 0.8481722063

Subproblem 2

b + -0.2234042553 = -0.624767951 Simplifying b + -0.2234042553 = -0.624767951 Reorder the terms: -0.2234042553 + b = -0.624767951 Solving -0.2234042553 + b = -0.624767951 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2234042553' to each side of the equation. -0.2234042553 + 0.2234042553 + b = -0.624767951 + 0.2234042553 Combine like terms: -0.2234042553 + 0.2234042553 = 0.0000000000 0.0000000000 + b = -0.624767951 + 0.2234042553 b = -0.624767951 + 0.2234042553 Combine like terms: -0.624767951 + 0.2234042553 = -0.4013636957 b = -0.4013636957 Simplifying b = -0.4013636957

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.8481722063, -0.4013636957}

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