10b^2-8b-7=0

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Solution for 10b^2-8b-7=0 equation: 


Simplifying
10b2 + -8b + -7 = 0

Reorder the terms:
-7 + -8b + 10b2 = 0

Solving
-7 + -8b + 10b2 = 0

Solving for variable 'b'.

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

Divide each side by '10'.
-0.7 + -0.8b + b2 = 0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + -0.8b + 0.7 + b2 = 0 + 0.7

Reorder the terms:
-0.7 + 0.7 + -0.8b + b2 = 0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + -0.8b + b2 = 0 + 0.7
-0.8b + b2 = 0 + 0.7

Combine like terms: 0 + 0.7 = 0.7
-0.8b + b2 = 0.7

The b term is -0.8b.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8b + 0.16 + b2 = 0.7 + 0.16

Reorder the terms:
0.16 + -0.8b + b2 = 0.7 + 0.16

Combine like terms: 0.7 + 0.16 = 0.86
0.16 + -0.8b + b2 = 0.86

Factor a perfect square on the left side:
(b + -0.4)(b + -0.4) = 0.86

Calculate the square root of the right side: 0.92736185

Break this problem into two subproblems by setting 
(b + -0.4) equal to 0.92736185 and -0.92736185.


Subproblem 1
b + -0.4 = 0.92736185

Simplifying
b + -0.4 = 0.92736185

Reorder the terms:
-0.4 + b = 0.92736185

Solving
-0.4 + b = 0.92736185

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '0.4' to each side of the equation.
-0.4 + 0.4 + b = 0.92736185 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + b = 0.92736185 + 0.4
b = 0.92736185 + 0.4

Combine like terms: 0.92736185 + 0.4 = 1.32736185
b = 1.32736185

Simplifying
b = 1.32736185


Subproblem 2
b + -0.4 = -0.92736185

Simplifying
b + -0.4 = -0.92736185

Reorder the terms:
-0.4 + b = -0.92736185

Solving
-0.4 + b = -0.92736185

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '0.4' to each side of the equation.
-0.4 + 0.4 + b = -0.92736185 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + b = -0.92736185 + 0.4
b = -0.92736185 + 0.4

Combine like terms: -0.92736185 + 0.4 = -0.52736185
b = -0.52736185

Simplifying
b = -0.52736185


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.32736185, -0.52736185}

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