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Simplifying 2b2 + -6b + -13 = 0 Reorder the terms: -13 + -6b + 2b2 = 0 Solving -13 + -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'. -6.5 + -3b + b2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -3b + 6.5 + b2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -3b + b2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -3b + b2 = 0 + 6.5 -3b + b2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -3b + b2 = 6.5 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 = 6.5 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 6.5 + 2.25 Combine like terms: 6.5 + 2.25 = 8.75 2.25 + -3b + b2 = 8.75 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (b + -1.5) equal to 2.958039892 and -2.958039892.Subproblem 1
b + -1.5 = 2.958039892 Simplifying b + -1.5 = 2.958039892 Reorder the terms: -1.5 + b = 2.958039892 Solving -1.5 + b = 2.958039892 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 = 2.958039892 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 2.958039892 + 1.5 b = 2.958039892 + 1.5 Combine like terms: 2.958039892 + 1.5 = 4.458039892 b = 4.458039892 Simplifying b = 4.458039892Subproblem 2
b + -1.5 = -2.958039892 Simplifying b + -1.5 = -2.958039892 Reorder the terms: -1.5 + b = -2.958039892 Solving -1.5 + b = -2.958039892 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 = -2.958039892 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -2.958039892 + 1.5 b = -2.958039892 + 1.5 Combine like terms: -2.958039892 + 1.5 = -1.458039892 b = -1.458039892 Simplifying b = -1.458039892Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.458039892, -1.458039892}
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