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Simplifying b(5b + -3) = 1 Reorder the terms: b(-3 + 5b) = 1 (-3 * b + 5b * b) = 1 (-3b + 5b2) = 1 Solving -3b + 5b2 = 1 Solving for variable 'b'. Reorder the terms: -1 + -3b + 5b2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -3b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.6b + b2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.6b + 0.2 + b2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.6b + b2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.6b + b2 = 0 + 0.2 -0.6b + b2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.6b + b2 = 0.2 The b term is -0.6b. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6b + 0.09 + b2 = 0.2 + 0.09 Reorder the terms: 0.09 + -0.6b + b2 = 0.2 + 0.09 Combine like terms: 0.2 + 0.09 = 0.29 0.09 + -0.6b + b2 = 0.29 Factor a perfect square on the left side: (b + -0.3)(b + -0.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (b + -0.3) equal to 0.538516481 and -0.538516481.Subproblem 1
b + -0.3 = 0.538516481 Simplifying b + -0.3 = 0.538516481 Reorder the terms: -0.3 + b = 0.538516481 Solving -0.3 + b = 0.538516481 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + b = 0.538516481 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + b = 0.538516481 + 0.3 b = 0.538516481 + 0.3 Combine like terms: 0.538516481 + 0.3 = 0.838516481 b = 0.838516481 Simplifying b = 0.838516481Subproblem 2
b + -0.3 = -0.538516481 Simplifying b + -0.3 = -0.538516481 Reorder the terms: -0.3 + b = -0.538516481 Solving -0.3 + b = -0.538516481 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + b = -0.538516481 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + b = -0.538516481 + 0.3 b = -0.538516481 + 0.3 Combine like terms: -0.538516481 + 0.3 = -0.238516481 b = -0.238516481 Simplifying b = -0.238516481Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.838516481, -0.238516481}
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