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Simplifying 10b2 + -1 = -2b Reorder the terms: -1 + 10b2 = -2b Solving -1 + 10b2 = -2b Solving for variable 'b'. Reorder the terms: -1 + 2b + 10b2 = -2b + 2b Combine like terms: -2b + 2b = 0 -1 + 2b + 10b2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + 0.2b + b2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.2b + 0.1 + b2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.2b + b2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.2b + b2 = 0 + 0.1 0.2b + b2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.2b + b2 = 0.1 The b term is 0.2b. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2b + 0.01 + b2 = 0.1 + 0.01 Reorder the terms: 0.01 + 0.2b + b2 = 0.1 + 0.01 Combine like terms: 0.1 + 0.01 = 0.11 0.01 + 0.2b + b2 = 0.11 Factor a perfect square on the left side: (b + 0.1)(b + 0.1) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (b + 0.1) equal to 0.331662479 and -0.331662479.Subproblem 1
b + 0.1 = 0.331662479 Simplifying b + 0.1 = 0.331662479 Reorder the terms: 0.1 + b = 0.331662479 Solving 0.1 + b = 0.331662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + b = 0.331662479 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + b = 0.331662479 + -0.1 b = 0.331662479 + -0.1 Combine like terms: 0.331662479 + -0.1 = 0.231662479 b = 0.231662479 Simplifying b = 0.231662479Subproblem 2
b + 0.1 = -0.331662479 Simplifying b + 0.1 = -0.331662479 Reorder the terms: 0.1 + b = -0.331662479 Solving 0.1 + b = -0.331662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + b = -0.331662479 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + b = -0.331662479 + -0.1 b = -0.331662479 + -0.1 Combine like terms: -0.331662479 + -0.1 = -0.431662479 b = -0.431662479 Simplifying b = -0.431662479Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.231662479, -0.431662479}
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