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Simplifying b(b + 2) = 144 Reorder the terms: b(2 + b) = 144 (2 * b + b * b) = 144 (2b + b2) = 144 Solving 2b + b2 = 144 Solving for variable 'b'. Reorder the terms: -144 + 2b + b2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 2b + 144 + b2 = 0 + 144 Reorder the terms: -144 + 144 + 2b + b2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 2b + b2 = 0 + 144 2b + b2 = 0 + 144 Combine like terms: 0 + 144 = 144 2b + b2 = 144 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 = 144 + 1 Reorder the terms: 1 + 2b + b2 = 144 + 1 Combine like terms: 144 + 1 = 145 1 + 2b + b2 = 145 Factor a perfect square on the left side: (b + 1)(b + 1) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (b + 1) equal to 12.041594579 and -12.041594579.Subproblem 1
b + 1 = 12.041594579 Simplifying b + 1 = 12.041594579 Reorder the terms: 1 + b = 12.041594579 Solving 1 + b = 12.041594579 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 = 12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + b = 12.041594579 + -1 b = 12.041594579 + -1 Combine like terms: 12.041594579 + -1 = 11.041594579 b = 11.041594579 Simplifying b = 11.041594579Subproblem 2
b + 1 = -12.041594579 Simplifying b + 1 = -12.041594579 Reorder the terms: 1 + b = -12.041594579 Solving 1 + b = -12.041594579 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 = -12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + b = -12.041594579 + -1 b = -12.041594579 + -1 Combine like terms: -12.041594579 + -1 = -13.041594579 b = -13.041594579 Simplifying b = -13.041594579Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.041594579, -13.041594579}
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