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Simplifying 10b2 + -10b + -2 = 0 Reorder the terms: -2 + -10b + 10b2 = 0 Solving -2 + -10b + 10b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -5b + 5b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5b + 5b2)' equal to zero and attempt to solve: Simplifying -1 + -5b + 5b2 = 0 Solving -1 + -5b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -1b + b2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1b + 0.2 + b2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1b + b2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1b + b2 = 0 + 0.2 -1b + b2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1b + b2 = 0.2 The b term is -1b. 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. -1b + 0.25 + b2 = 0.2 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 0.25 + -1b + b2 = 0.45 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (b + -0.5) equal to 0.670820393 and -0.670820393.Subproblem 1
b + -0.5 = 0.670820393 Simplifying b + -0.5 = 0.670820393 Reorder the terms: -0.5 + b = 0.670820393 Solving -0.5 + b = 0.670820393 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 = 0.670820393 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 0.670820393 + 0.5 b = 0.670820393 + 0.5 Combine like terms: 0.670820393 + 0.5 = 1.170820393 b = 1.170820393 Simplifying b = 1.170820393Subproblem 2
b + -0.5 = -0.670820393 Simplifying b + -0.5 = -0.670820393 Reorder the terms: -0.5 + b = -0.670820393 Solving -0.5 + b = -0.670820393 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 = -0.670820393 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -0.670820393 + 0.5 b = -0.670820393 + 0.5 Combine like terms: -0.670820393 + 0.5 = -0.170820393 b = -0.170820393 Simplifying b = -0.170820393Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.170820393, -0.170820393}Solution
b = {1.170820393, -0.170820393}
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