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Simplifying 2b2 + 12b + -5 = 0 Reorder the terms: -5 + 12b + 2b2 = 0 Solving -5 + 12b + 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 + 6b + b2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 6b + 2.5 + b2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 6b + b2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 6b + b2 = 0 + 2.5 6b + b2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 6b + b2 = 2.5 The b term is 6b. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6b + 9 + b2 = 2.5 + 9 Reorder the terms: 9 + 6b + b2 = 2.5 + 9 Combine like terms: 2.5 + 9 = 11.5 9 + 6b + b2 = 11.5 Factor a perfect square on the left side: (b + 3)(b + 3) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (b + 3) equal to 3.391164992 and -3.391164992.Subproblem 1
b + 3 = 3.391164992 Simplifying b + 3 = 3.391164992 Reorder the terms: 3 + b = 3.391164992 Solving 3 + b = 3.391164992 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 3.391164992 + -3 Combine like terms: 3 + -3 = 0 0 + b = 3.391164992 + -3 b = 3.391164992 + -3 Combine like terms: 3.391164992 + -3 = 0.391164992 b = 0.391164992 Simplifying b = 0.391164992Subproblem 2
b + 3 = -3.391164992 Simplifying b + 3 = -3.391164992 Reorder the terms: 3 + b = -3.391164992 Solving 3 + b = -3.391164992 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = -3.391164992 + -3 Combine like terms: 3 + -3 = 0 0 + b = -3.391164992 + -3 b = -3.391164992 + -3 Combine like terms: -3.391164992 + -3 = -6.391164992 b = -6.391164992 Simplifying b = -6.391164992Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.391164992, -6.391164992}
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