-7b^2+10b-2=-7

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


Simplifying
-7b2 + 10b + -2 = -7

Reorder the terms:
-2 + 10b + -7b2 = -7

Solving
-2 + 10b + -7b2 = -7

Solving for variable 'b'.

Reorder the terms:
-2 + 7 + 10b + -7b2 = -7 + 7

Combine like terms: -2 + 7 = 5
5 + 10b + -7b2 = -7 + 7

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

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.7142857143 + -1.428571429b + b2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -1.428571429b + 0.7142857143 + b2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -1.428571429b + b2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -1.428571429b + b2 = 0 + 0.7142857143
-1.428571429b + b2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-1.428571429b + b2 = 0.7142857143

The b term is -1.428571429b.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429b + 0.5102040819 + b2 = 0.7142857143 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429b + b2 = 0.7142857143 + 0.5102040819

Combine like terms: 0.7142857143 + 0.5102040819 = 1.2244897962
0.5102040819 + -1.428571429b + b2 = 1.2244897962

Factor a perfect square on the left side:
(b + -0.7142857145)(b + -0.7142857145) = 1.2244897962

Calculate the square root of the right side: 1.10656667

Break this problem into two subproblems by setting 
(b + -0.7142857145) equal to 1.10656667 and -1.10656667.

Subproblem 1

b + -0.7142857145 = 1.10656667 Simplifying b + -0.7142857145 = 1.10656667 Reorder the terms: -0.7142857145 + b = 1.10656667 Solving -0.7142857145 + b = 1.10656667 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + b = 1.10656667 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + b = 1.10656667 + 0.7142857145 b = 1.10656667 + 0.7142857145 Combine like terms: 1.10656667 + 0.7142857145 = 1.8208523845 b = 1.8208523845 Simplifying b = 1.8208523845

Subproblem 2

b + -0.7142857145 = -1.10656667 Simplifying b + -0.7142857145 = -1.10656667 Reorder the terms: -0.7142857145 + b = -1.10656667 Solving -0.7142857145 + b = -1.10656667 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + b = -1.10656667 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + b = -1.10656667 + 0.7142857145 b = -1.10656667 + 0.7142857145 Combine like terms: -1.10656667 + 0.7142857145 = -0.3922809555 b = -0.3922809555 Simplifying b = -0.3922809555

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.8208523845, -0.3922809555}

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