7+b(5-5b)-10b=

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Solution for 7+b(5-5b)-10b= equation:


Simplifying
7 + b(5 + -5b) + -10b = 0
7 + (5 * b + -5b * b) + -10b = 0
7 + (5b + -5b2) + -10b = 0

Reorder the terms:
7 + 5b + -10b + -5b2 = 0

Combine like terms: 5b + -10b = -5b
7 + -5b + -5b2 = 0

Solving
7 + -5b + -5b2 = 0

Solving for variable 'b'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.4 + b + b2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + b + 1.4 + b2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + b + b2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + b + b2 = 0 + 1.4
b + b2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
b + b2 = 1.4

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.
 + 0.25 + b2 = 1.4 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b2 = 1.4 + 0.25

Combine like terms: 1.4 + 0.25 = 1.65
1.25 + b2 = 1.65

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 1.65

Calculate the square root of the right side: 1.284523258

Break this problem into two subproblems by setting 
(b + 0.5) equal to 1.284523258 and -1.284523258.

Subproblem 1

b + 0.5 = 1.284523258 Simplifying b + 0.5 = 1.284523258 Reorder the terms: 0.5 + b = 1.284523258 Solving 0.5 + b = 1.284523258 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 = 1.284523258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 1.284523258 + -0.5 b = 1.284523258 + -0.5 Combine like terms: 1.284523258 + -0.5 = 0.784523258 b = 0.784523258 Simplifying b = 0.784523258

Subproblem 2

b + 0.5 = -1.284523258 Simplifying b + 0.5 = -1.284523258 Reorder the terms: 0.5 + b = -1.284523258 Solving 0.5 + b = -1.284523258 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 = -1.284523258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -1.284523258 + -0.5 b = -1.284523258 + -0.5 Combine like terms: -1.284523258 + -0.5 = -1.784523258 b = -1.784523258 Simplifying b = -1.784523258

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.784523258, -1.784523258}

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