102b+b^2=3

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Solution for 102b+b^2=3 equation:


Simplifying
102b + b2 = 3

Solving
102b + b2 = 3

Solving for variable 'b'.

Reorder the terms:
-3 + 102b + b2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 102b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 102b + 3 + b2 = 0 + 3

Reorder the terms:
-3 + 3 + 102b + b2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 102b + b2 = 0 + 3
102b + b2 = 0 + 3

Combine like terms: 0 + 3 = 3
102b + b2 = 3

The b term is 102b.  Take half its coefficient (51).
Square it (2601) and add it to both sides.

Add '2601' to each side of the equation.
102b + 2601 + b2 = 3 + 2601

Reorder the terms:
2601 + 102b + b2 = 3 + 2601

Combine like terms: 3 + 2601 = 2604
2601 + 102b + b2 = 2604

Factor a perfect square on the left side:
(b + 51)(b + 51) = 2604

Calculate the square root of the right side: 51.029403289

Break this problem into two subproblems by setting 
(b + 51) equal to 51.029403289 and -51.029403289.

Subproblem 1

b + 51 = 51.029403289 Simplifying b + 51 = 51.029403289 Reorder the terms: 51 + b = 51.029403289 Solving 51 + b = 51.029403289 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + b = 51.029403289 + -51 Combine like terms: 51 + -51 = 0 0 + b = 51.029403289 + -51 b = 51.029403289 + -51 Combine like terms: 51.029403289 + -51 = 0.029403289 b = 0.029403289 Simplifying b = 0.029403289

Subproblem 2

b + 51 = -51.029403289 Simplifying b + 51 = -51.029403289 Reorder the terms: 51 + b = -51.029403289 Solving 51 + b = -51.029403289 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + b = -51.029403289 + -51 Combine like terms: 51 + -51 = 0 0 + b = -51.029403289 + -51 b = -51.029403289 + -51 Combine like terms: -51.029403289 + -51 = -102.029403289 b = -102.029403289 Simplifying b = -102.029403289

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.029403289, -102.029403289}

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