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Simplifying b(4 + b) = 99 (4 * b + b * b) = 99 (4b + b2) = 99 Solving 4b + b2 = 99 Solving for variable 'b'. Reorder the terms: -99 + 4b + b2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 4b + 99 + b2 = 0 + 99 Reorder the terms: -99 + 99 + 4b + b2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 4b + b2 = 0 + 99 4b + b2 = 0 + 99 Combine like terms: 0 + 99 = 99 4b + b2 = 99 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 = 99 + 4 Reorder the terms: 4 + 4b + b2 = 99 + 4 Combine like terms: 99 + 4 = 103 4 + 4b + b2 = 103 Factor a perfect square on the left side: (b + 2)(b + 2) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (b + 2) equal to 10.148891565 and -10.148891565.Subproblem 1
b + 2 = 10.148891565 Simplifying b + 2 = 10.148891565 Reorder the terms: 2 + b = 10.148891565 Solving 2 + b = 10.148891565 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 = 10.148891565 + -2 Combine like terms: 2 + -2 = 0 0 + b = 10.148891565 + -2 b = 10.148891565 + -2 Combine like terms: 10.148891565 + -2 = 8.148891565 b = 8.148891565 Simplifying b = 8.148891565Subproblem 2
b + 2 = -10.148891565 Simplifying b + 2 = -10.148891565 Reorder the terms: 2 + b = -10.148891565 Solving 2 + b = -10.148891565 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 = -10.148891565 + -2 Combine like terms: 2 + -2 = 0 0 + b = -10.148891565 + -2 b = -10.148891565 + -2 Combine like terms: -10.148891565 + -2 = -12.148891565 b = -12.148891565 Simplifying b = -12.148891565Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.148891565, -12.148891565}
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