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Simplifying b2 = 3 + -4b Solving b2 = 3 + -4b Solving for variable 'b'. Reorder the terms: -3 + 4b + b2 = 3 + -4b + -3 + 4b Reorder the terms: -3 + 4b + b2 = 3 + -3 + -4b + 4b Combine like terms: 3 + -3 = 0 -3 + 4b + b2 = 0 + -4b + 4b -3 + 4b + b2 = -4b + 4b Combine like terms: -4b + 4b = 0 -3 + 4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + 4b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4b + b2 = 0 + 3 4b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 4b + b2 = 3 The b term is 4b. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4b + 4 + b2 = 3 + 4 Reorder the terms: 4 + 4b + b2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4b + b2 = 7 Factor a perfect square on the left side: (b + 2)(b + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (b + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
b + 2 = 2.645751311 Simplifying b + 2 = 2.645751311 Reorder the terms: 2 + b = 2.645751311 Solving 2 + b = 2.645751311 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + b = 2.645751311 + -2 b = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 b = 0.645751311 Simplifying b = 0.645751311Subproblem 2
b + 2 = -2.645751311 Simplifying b + 2 = -2.645751311 Reorder the terms: 2 + b = -2.645751311 Solving 2 + b = -2.645751311 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + b = -2.645751311 + -2 b = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 b = -4.645751311 Simplifying b = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.645751311, -4.645751311}
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