-10b^2+b=-7

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Solution for -10b^2+b=-7 equation:


Simplifying
-10b2 + b = -7

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

Solving
b + -10b2 = -7

Solving for variable 'b'.

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

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

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

Divide each side by '-10'.
-0.7 + -0.1b + b2 = 0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + -0.1b + 0.7 + b2 = 0 + 0.7

Reorder the terms:
-0.7 + 0.7 + -0.1b + b2 = 0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + -0.1b + b2 = 0 + 0.7
-0.1b + b2 = 0 + 0.7

Combine like terms: 0 + 0.7 = 0.7
-0.1b + b2 = 0.7

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.
-0.1b + 0.25 + b2 = 0.7 + 0.25

Reorder the terms:
0.25 + -0.1b + b2 = 0.7 + 0.25

Combine like terms: 0.7 + 0.25 = 0.95
0.25 + -0.1b + b2 = 0.95

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.95

Calculate the square root of the right side: 0.974679434

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.974679434 and -0.974679434.

Subproblem 1

b + 0.5 = 0.974679434 Simplifying b + 0.5 = 0.974679434 Reorder the terms: 0.5 + b = 0.974679434 Solving 0.5 + b = 0.974679434 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 = 0.974679434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 0.974679434 + -0.5 b = 0.974679434 + -0.5 Combine like terms: 0.974679434 + -0.5 = 0.474679434 b = 0.474679434 Simplifying b = 0.474679434

Subproblem 2

b + 0.5 = -0.974679434 Simplifying b + 0.5 = -0.974679434 Reorder the terms: 0.5 + b = -0.974679434 Solving 0.5 + b = -0.974679434 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 = -0.974679434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -0.974679434 + -0.5 b = -0.974679434 + -0.5 Combine like terms: -0.974679434 + -0.5 = -1.474679434 b = -1.474679434 Simplifying b = -1.474679434

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.474679434, -1.474679434}

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