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Simplifying b2 + 4b + -22 = 0 Reorder the terms: -22 + 4b + b2 = 0 Solving -22 + 4b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 4b + 22 + b2 = 0 + 22 Reorder the terms: -22 + 22 + 4b + b2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 4b + b2 = 0 + 22 4b + b2 = 0 + 22 Combine like terms: 0 + 22 = 22 4b + b2 = 22 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 = 22 + 4 Reorder the terms: 4 + 4b + b2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + 4b + b2 = 26 Factor a perfect square on the left side: (b + 2)(b + 2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (b + 2) equal to 5.099019514 and -5.099019514.Subproblem 1
b + 2 = 5.099019514 Simplifying b + 2 = 5.099019514 Reorder the terms: 2 + b = 5.099019514 Solving 2 + b = 5.099019514 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 = 5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + b = 5.099019514 + -2 b = 5.099019514 + -2 Combine like terms: 5.099019514 + -2 = 3.099019514 b = 3.099019514 Simplifying b = 3.099019514Subproblem 2
b + 2 = -5.099019514 Simplifying b + 2 = -5.099019514 Reorder the terms: 2 + b = -5.099019514 Solving 2 + b = -5.099019514 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 = -5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + b = -5.099019514 + -2 b = -5.099019514 + -2 Combine like terms: -5.099019514 + -2 = -7.099019514 b = -7.099019514 Simplifying b = -7.099019514Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.099019514, -7.099019514}
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