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Simplifying 2b2 + -7b + 2 = 0 Reorder the terms: 2 + -7b + 2b2 = 0 Solving 2 + -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 + -3.5b + b2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.5b + -1 + b2 = 0 + -1 Reorder the terms: 1 + -1 + -3.5b + b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.5b + b2 = 0 + -1 -3.5b + b2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.5b + b2 = -1 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 + 3.0625 Reorder the terms: 3.0625 + -3.5b + b2 = -1 + 3.0625 Combine like terms: -1 + 3.0625 = 2.0625 3.0625 + -3.5b + b2 = 2.0625 Factor a perfect square on the left side: (b + -1.75)(b + -1.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (b + -1.75) equal to 1.436140662 and -1.436140662.Subproblem 1
b + -1.75 = 1.436140662 Simplifying b + -1.75 = 1.436140662 Reorder the terms: -1.75 + b = 1.436140662 Solving -1.75 + b = 1.436140662 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 = 1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + b = 1.436140662 + 1.75 b = 1.436140662 + 1.75 Combine like terms: 1.436140662 + 1.75 = 3.186140662 b = 3.186140662 Simplifying b = 3.186140662Subproblem 2
b + -1.75 = -1.436140662 Simplifying b + -1.75 = -1.436140662 Reorder the terms: -1.75 + b = -1.436140662 Solving -1.75 + b = -1.436140662 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 = -1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + b = -1.436140662 + 1.75 b = -1.436140662 + 1.75 Combine like terms: -1.436140662 + 1.75 = 0.313859338 b = 0.313859338 Simplifying b = 0.313859338Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.186140662, 0.313859338}
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