b^2-7b=11

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Solution for b^2-7b=11 equation:


Simplifying
b2 + -7b = 11

Reorder the terms:
-7b + b2 = 11

Solving
-7b + b2 = 11

Solving for variable 'b'.

Reorder the terms:
-11 + -7b + b2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -7b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -7b + 11 + b2 = 0 + 11

Reorder the terms:
-11 + 11 + -7b + b2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -7b + b2 = 0 + 11
-7b + b2 = 0 + 11

Combine like terms: 0 + 11 = 11
-7b + b2 = 11

The b term is -7b.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7b + 12.25 + b2 = 11 + 12.25

Reorder the terms:
12.25 + -7b + b2 = 11 + 12.25

Combine like terms: 11 + 12.25 = 23.25
12.25 + -7b + b2 = 23.25

Factor a perfect square on the left side:
(b + -3.5)(b + -3.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(b + -3.5) equal to 4.82182538 and -4.82182538.

Subproblem 1

b + -3.5 = 4.82182538 Simplifying b + -3.5 = 4.82182538 Reorder the terms: -3.5 + b = 4.82182538 Solving -3.5 + b = 4.82182538 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b = 4.82182538 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = 4.82182538 + 3.5 b = 4.82182538 + 3.5 Combine like terms: 4.82182538 + 3.5 = 8.32182538 b = 8.32182538 Simplifying b = 8.32182538

Subproblem 2

b + -3.5 = -4.82182538 Simplifying b + -3.5 = -4.82182538 Reorder the terms: -3.5 + b = -4.82182538 Solving -3.5 + b = -4.82182538 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b = -4.82182538 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = -4.82182538 + 3.5 b = -4.82182538 + 3.5 Combine like terms: -4.82182538 + 3.5 = -1.32182538 b = -1.32182538 Simplifying b = -1.32182538

Solution

The solution to the problem is based on the solutions from the subproblems. b = {8.32182538, -1.32182538}

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