b^2+b-62=0

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Solution for b^2+b-62=0 equation:


Simplifying
b2 + b + -62 = 0

Reorder the terms:
-62 + b + b2 = 0

Solving
-62 + b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + b + 62 + b2 = 0 + 62

Reorder the terms:
-62 + 62 + b + b2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + b + b2 = 0 + 62
b + b2 = 0 + 62

Combine like terms: 0 + 62 = 62
b + b2 = 62

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

Add '0.25' to each side of the equation.
b + 0.25 + b2 = 62 + 0.25

Reorder the terms:
0.25 + b + b2 = 62 + 0.25

Combine like terms: 62 + 0.25 = 62.25
0.25 + b + b2 = 62.25

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(b + 0.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

b + 0.5 = 7.889866919 Simplifying b + 0.5 = 7.889866919 Reorder the terms: 0.5 + b = 7.889866919 Solving 0.5 + b = 7.889866919 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 7.889866919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 7.889866919 + -0.5 b = 7.889866919 + -0.5 Combine like terms: 7.889866919 + -0.5 = 7.389866919 b = 7.389866919 Simplifying b = 7.389866919

Subproblem 2

b + 0.5 = -7.889866919 Simplifying b + 0.5 = -7.889866919 Reorder the terms: 0.5 + b = -7.889866919 Solving 0.5 + b = -7.889866919 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -7.889866919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -7.889866919 + -0.5 b = -7.889866919 + -0.5 Combine like terms: -7.889866919 + -0.5 = -8.389866919 b = -8.389866919 Simplifying b = -8.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. b = {7.389866919, -8.389866919}

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