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Simplifying (2 + -1B) * B = 0.13 Reorder the terms for easier multiplication: B(2 + -1B) = 0.13 (2 * B + -1B * B) = 0.13 (2B + -1B2) = 0.13 Solving 2B + -1B2 = 0.13 Solving for variable 'B'. Reorder the terms: -0.13 + 2B + -1B2 = 0.13 + -0.13 Combine like terms: 0.13 + -0.13 = 0.00 -0.13 + 2B + -1B2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.13 + -2B + B2 = 0.00 Move the constant term to the right: Add '-0.13' to each side of the equation. 0.13 + -2B + -0.13 + B2 = 0.00 + -0.13 Reorder the terms: 0.13 + -0.13 + -2B + B2 = 0.00 + -0.13 Combine like terms: 0.13 + -0.13 = 0.00 0.00 + -2B + B2 = 0.00 + -0.13 -2B + B2 = 0.00 + -0.13 Combine like terms: 0.00 + -0.13 = -0.13 -2B + B2 = -0.13 The B term is -2B. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2B + 1 + B2 = -0.13 + 1 Reorder the terms: 1 + -2B + B2 = -0.13 + 1 Combine like terms: -0.13 + 1 = 0.87 1 + -2B + B2 = 0.87 Factor a perfect square on the left side: (B + -1)(B + -1) = 0.87 Calculate the square root of the right side: 0.932737905 Break this problem into two subproblems by setting (B + -1) equal to 0.932737905 and -0.932737905.Subproblem 1
B + -1 = 0.932737905 Simplifying B + -1 = 0.932737905 Reorder the terms: -1 + B = 0.932737905 Solving -1 + B = 0.932737905 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + B = 0.932737905 + 1 Combine like terms: -1 + 1 = 0 0 + B = 0.932737905 + 1 B = 0.932737905 + 1 Combine like terms: 0.932737905 + 1 = 1.932737905 B = 1.932737905 Simplifying B = 1.932737905Subproblem 2
B + -1 = -0.932737905 Simplifying B + -1 = -0.932737905 Reorder the terms: -1 + B = -0.932737905 Solving -1 + B = -0.932737905 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + B = -0.932737905 + 1 Combine like terms: -1 + 1 = 0 0 + B = -0.932737905 + 1 B = -0.932737905 + 1 Combine like terms: -0.932737905 + 1 = 0.067262095 B = 0.067262095 Simplifying B = 0.067262095Solution
The solution to the problem is based on the solutions from the subproblems. B = {1.932737905, 0.067262095}
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