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Simplifying 2b2 + -19b + 36 = 0 Reorder the terms: 36 + -19b + 2b2 = 0 Solving 36 + -19b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + -9.5b + b2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -9.5b + -18 + b2 = 0 + -18 Reorder the terms: 18 + -18 + -9.5b + b2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -9.5b + b2 = 0 + -18 -9.5b + b2 = 0 + -18 Combine like terms: 0 + -18 = -18 -9.5b + b2 = -18 The b term is -9.5b. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5b + 22.5625 + b2 = -18 + 22.5625 Reorder the terms: 22.5625 + -9.5b + b2 = -18 + 22.5625 Combine like terms: -18 + 22.5625 = 4.5625 22.5625 + -9.5b + b2 = 4.5625 Factor a perfect square on the left side: (b + -4.75)(b + -4.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (b + -4.75) equal to 2.136000936 and -2.136000936.Subproblem 1
b + -4.75 = 2.136000936 Simplifying b + -4.75 = 2.136000936 Reorder the terms: -4.75 + b = 2.136000936 Solving -4.75 + b = 2.136000936 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + b = 2.136000936 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + b = 2.136000936 + 4.75 b = 2.136000936 + 4.75 Combine like terms: 2.136000936 + 4.75 = 6.886000936 b = 6.886000936 Simplifying b = 6.886000936Subproblem 2
b + -4.75 = -2.136000936 Simplifying b + -4.75 = -2.136000936 Reorder the terms: -4.75 + b = -2.136000936 Solving -4.75 + b = -2.136000936 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + b = -2.136000936 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + b = -2.136000936 + 4.75 b = -2.136000936 + 4.75 Combine like terms: -2.136000936 + 4.75 = 2.613999064 b = 2.613999064 Simplifying b = 2.613999064Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.886000936, 2.613999064}
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