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Simplifying 2b2 + 6b + -5 = 0 Reorder the terms: -5 + 6b + 2b2 = 0 Solving -5 + 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'. -2.5 + 3b + b2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3b + 2.5 + b2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3b + b2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3b + b2 = 0 + 2.5 3b + b2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3b + b2 = 2.5 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 = 2.5 + 2.25 Reorder the terms: 2.25 + 3b + b2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + 3b + b2 = 4.75 Factor a perfect square on the left side: (b + 1.5)(b + 1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (b + 1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
b + 1.5 = 2.179449472 Simplifying b + 1.5 = 2.179449472 Reorder the terms: 1.5 + b = 2.179449472 Solving 1.5 + b = 2.179449472 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 = 2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 2.179449472 + -1.5 b = 2.179449472 + -1.5 Combine like terms: 2.179449472 + -1.5 = 0.679449472 b = 0.679449472 Simplifying b = 0.679449472Subproblem 2
b + 1.5 = -2.179449472 Simplifying b + 1.5 = -2.179449472 Reorder the terms: 1.5 + b = -2.179449472 Solving 1.5 + b = -2.179449472 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 = -2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -2.179449472 + -1.5 b = -2.179449472 + -1.5 Combine like terms: -2.179449472 + -1.5 = -3.679449472 b = -3.679449472 Simplifying b = -3.679449472Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.679449472, -3.679449472}
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