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Simplifying 2b2 + 6b + -1 = 0 Reorder the terms: -1 + 6b + 2b2 = 0 Solving -1 + 6b + 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'. -0.5 + 3b + b2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 3b + 0.5 + b2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 3b + b2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 3b + b2 = 0 + 0.5 3b + b2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 3b + b2 = 0.5 The b term is 3b. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3b + 2.25 + b2 = 0.5 + 2.25 Reorder the terms: 2.25 + 3b + b2 = 0.5 + 2.25 Combine like terms: 0.5 + 2.25 = 2.75 2.25 + 3b + b2 = 2.75 Factor a perfect square on the left side: (b + 1.5)(b + 1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (b + 1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
b + 1.5 = 1.658312395 Simplifying b + 1.5 = 1.658312395 Reorder the terms: 1.5 + b = 1.658312395 Solving 1.5 + b = 1.658312395 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 1.658312395 + -1.5 b = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 b = 0.158312395 Simplifying b = 0.158312395Subproblem 2
b + 1.5 = -1.658312395 Simplifying b + 1.5 = -1.658312395 Reorder the terms: 1.5 + b = -1.658312395 Solving 1.5 + b = -1.658312395 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -1.658312395 + -1.5 b = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 b = -3.158312395 Simplifying b = -3.158312395Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.158312395, -3.158312395}
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