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Simplifying 2b2 + -7b + -3 = 0 Reorder the terms: -3 + -7b + 2b2 = 0 Solving -3 + -7b + 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'. -1.5 + -3.5b + b2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.5b + 1.5 + b2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.5b + b2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.5b + b2 = 0 + 1.5 -3.5b + b2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.5b + b2 = 1.5 The b term is -3.5b. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5b + 3.0625 + b2 = 1.5 + 3.0625 Reorder the terms: 3.0625 + -3.5b + b2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + -3.5b + b2 = 4.5625 Factor a perfect square on the left side: (b + -1.75)(b + -1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (b + -1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
b + -1.75 = 2.136000936 Simplifying b + -1.75 = 2.136000936 Reorder the terms: -1.75 + b = 2.136000936 Solving -1.75 + b = 2.136000936 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + b = 2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + b = 2.136000936 + 1.75 b = 2.136000936 + 1.75 Combine like terms: 2.136000936 + 1.75 = 3.886000936 b = 3.886000936 Simplifying b = 3.886000936Subproblem 2
b + -1.75 = -2.136000936 Simplifying b + -1.75 = -2.136000936 Reorder the terms: -1.75 + b = -2.136000936 Solving -1.75 + b = -2.136000936 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + b = -2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + b = -2.136000936 + 1.75 b = -2.136000936 + 1.75 Combine like terms: -2.136000936 + 1.75 = -0.386000936 b = -0.386000936 Simplifying b = -0.386000936Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.886000936, -0.386000936}
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