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Simplifying 3b2 + 6b + -22 = 0 Reorder the terms: -22 + 6b + 3b2 = 0 Solving -22 + 6b + 3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + 2b + b2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + 2b + 7.333333333 + b2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + 2b + b2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + 2b + b2 = 0 + 7.333333333 2b + b2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 2b + b2 = 7.333333333 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = 7.333333333 + 1 Reorder the terms: 1 + 2b + b2 = 7.333333333 + 1 Combine like terms: 7.333333333 + 1 = 8.333333333 1 + 2b + b2 = 8.333333333 Factor a perfect square on the left side: (b + 1)(b + 1) = 8.333333333 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (b + 1) equal to 2.886751346 and -2.886751346.Subproblem 1
b + 1 = 2.886751346 Simplifying b + 1 = 2.886751346 Reorder the terms: 1 + b = 2.886751346 Solving 1 + b = 2.886751346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 2.886751346 + -1 Combine like terms: 1 + -1 = 0 0 + b = 2.886751346 + -1 b = 2.886751346 + -1 Combine like terms: 2.886751346 + -1 = 1.886751346 b = 1.886751346 Simplifying b = 1.886751346Subproblem 2
b + 1 = -2.886751346 Simplifying b + 1 = -2.886751346 Reorder the terms: 1 + b = -2.886751346 Solving 1 + b = -2.886751346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -2.886751346 + -1 Combine like terms: 1 + -1 = 0 0 + b = -2.886751346 + -1 b = -2.886751346 + -1 Combine like terms: -2.886751346 + -1 = -3.886751346 b = -3.886751346 Simplifying b = -3.886751346Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.886751346, -3.886751346}
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