(b-3)b=35

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Solution for (b-3)b=35 equation:


Simplifying
(b + -3) * b = 35

Reorder the terms:
(-3 + b) * b = 35

Reorder the terms for easier multiplication:
b(-3 + b) = 35
(-3 * b + b * b) = 35
(-3b + b2) = 35

Solving
-3b + b2 = 35

Solving for variable 'b'.

Reorder the terms:
-35 + -3b + b2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -3b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -3b + 35 + b2 = 0 + 35

Reorder the terms:
-35 + 35 + -3b + b2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -3b + b2 = 0 + 35
-3b + b2 = 0 + 35

Combine like terms: 0 + 35 = 35
-3b + b2 = 35

The b term is -3b.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3b + 2.25 + b2 = 35 + 2.25

Reorder the terms:
2.25 + -3b + b2 = 35 + 2.25

Combine like terms: 35 + 2.25 = 37.25
2.25 + -3b + b2 = 37.25

Factor a perfect square on the left side:
(b + -1.5)(b + -1.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(b + -1.5) equal to 6.103277808 and -6.103277808.

Subproblem 1

b + -1.5 = 6.103277808 Simplifying b + -1.5 = 6.103277808 Reorder the terms: -1.5 + b = 6.103277808 Solving -1.5 + b = 6.103277808 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 6.103277808 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 6.103277808 + 1.5 b = 6.103277808 + 1.5 Combine like terms: 6.103277808 + 1.5 = 7.603277808 b = 7.603277808 Simplifying b = 7.603277808

Subproblem 2

b + -1.5 = -6.103277808 Simplifying b + -1.5 = -6.103277808 Reorder the terms: -1.5 + b = -6.103277808 Solving -1.5 + b = -6.103277808 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -6.103277808 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -6.103277808 + 1.5 b = -6.103277808 + 1.5 Combine like terms: -6.103277808 + 1.5 = -4.603277808 b = -4.603277808 Simplifying b = -4.603277808

Solution

The solution to the problem is based on the solutions from the subproblems. b = {7.603277808, -4.603277808}

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