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Simplifying (4b)(4b) + 13b + -12 = 0 Remove parenthesis around (4b) 4b(4b) + 13b + -12 = 0 Remove parenthesis around (4b) 4b * 4b + 13b + -12 = 0 Reorder the terms for easier multiplication: 4 * 4b * b + 13b + -12 = 0 Multiply 4 * 4 16b * b + 13b + -12 = 0 Multiply b * b 16b2 + 13b + -12 = 0 Reorder the terms: -12 + 13b + 16b2 = 0 Solving -12 + 13b + 16b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.75 + 0.8125b + b2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.8125b + 0.75 + b2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.8125b + b2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.8125b + b2 = 0 + 0.75 0.8125b + b2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.8125b + b2 = 0.75 The b term is 0.8125b. Take half its coefficient (0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. 0.8125b + 0.1650390625 + b2 = 0.75 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125b + b2 = 0.75 + 0.1650390625 Combine like terms: 0.75 + 0.1650390625 = 0.9150390625 0.1650390625 + 0.8125b + b2 = 0.9150390625 Factor a perfect square on the left side: (b + 0.40625)(b + 0.40625) = 0.9150390625 Calculate the square root of the right side: 0.956576742 Break this problem into two subproblems by setting (b + 0.40625) equal to 0.956576742 and -0.956576742.Subproblem 1
b + 0.40625 = 0.956576742 Simplifying b + 0.40625 = 0.956576742 Reorder the terms: 0.40625 + b = 0.956576742 Solving 0.40625 + b = 0.956576742 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + b = 0.956576742 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + b = 0.956576742 + -0.40625 b = 0.956576742 + -0.40625 Combine like terms: 0.956576742 + -0.40625 = 0.550326742 b = 0.550326742 Simplifying b = 0.550326742Subproblem 2
b + 0.40625 = -0.956576742 Simplifying b + 0.40625 = -0.956576742 Reorder the terms: 0.40625 + b = -0.956576742 Solving 0.40625 + b = -0.956576742 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + b = -0.956576742 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + b = -0.956576742 + -0.40625 b = -0.956576742 + -0.40625 Combine like terms: -0.956576742 + -0.40625 = -1.362826742 b = -1.362826742 Simplifying b = -1.362826742Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.550326742, -1.362826742}
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