b^2-7b+4=0

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Solution for b^2-7b+4=0 equation:


Simplifying
b2 + -7b + 4 = 0

Reorder the terms:
4 + -7b + b2 = 0

Solving
4 + -7b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7b + -4 + b2 = 0 + -4

Reorder the terms:
4 + -4 + -7b + b2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7b + b2 = 0 + -4
-7b + b2 = 0 + -4

Combine like terms: 0 + -4 = -4
-7b + b2 = -4

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 = -4 + 12.25

Reorder the terms:
12.25 + -7b + b2 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + -7b + b2 = 8.25

Factor a perfect square on the left side:
(b + -3.5)(b + -3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(b + -3.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

b + -3.5 = 2.872281323 Simplifying b + -3.5 = 2.872281323 Reorder the terms: -3.5 + b = 2.872281323 Solving -3.5 + b = 2.872281323 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 = 2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = 2.872281323 + 3.5 b = 2.872281323 + 3.5 Combine like terms: 2.872281323 + 3.5 = 6.372281323 b = 6.372281323 Simplifying b = 6.372281323

Subproblem 2

b + -3.5 = -2.872281323 Simplifying b + -3.5 = -2.872281323 Reorder the terms: -3.5 + b = -2.872281323 Solving -3.5 + b = -2.872281323 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 = -2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = -2.872281323 + 3.5 b = -2.872281323 + 3.5 Combine like terms: -2.872281323 + 3.5 = 0.627718677 b = 0.627718677 Simplifying b = 0.627718677

Solution

The solution to the problem is based on the solutions from the subproblems. b = {6.372281323, 0.627718677}

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