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Simplifying 2b2 + -7b + 4 = 0 Reorder the terms: 4 + -7b + 2b2 = 0 Solving 4 + -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'. 2 + -3.5b + b2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.5b + -2 + b2 = 0 + -2 Reorder the terms: 2 + -2 + -3.5b + b2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.5b + b2 = 0 + -2 -3.5b + b2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.5b + b2 = -2 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 = -2 + 3.0625 Reorder the terms: 3.0625 + -3.5b + b2 = -2 + 3.0625 Combine like terms: -2 + 3.0625 = 1.0625 3.0625 + -3.5b + b2 = 1.0625 Factor a perfect square on the left side: (b + -1.75)(b + -1.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (b + -1.75) equal to 1.030776406 and -1.030776406.Subproblem 1
b + -1.75 = 1.030776406 Simplifying b + -1.75 = 1.030776406 Reorder the terms: -1.75 + b = 1.030776406 Solving -1.75 + b = 1.030776406 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 = 1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + b = 1.030776406 + 1.75 b = 1.030776406 + 1.75 Combine like terms: 1.030776406 + 1.75 = 2.780776406 b = 2.780776406 Simplifying b = 2.780776406Subproblem 2
b + -1.75 = -1.030776406 Simplifying b + -1.75 = -1.030776406 Reorder the terms: -1.75 + b = -1.030776406 Solving -1.75 + b = -1.030776406 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 = -1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + b = -1.030776406 + 1.75 b = -1.030776406 + 1.75 Combine like terms: -1.030776406 + 1.75 = 0.719223594 b = 0.719223594 Simplifying b = 0.719223594Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.780776406, 0.719223594}
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