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Simplifying 120 = 10b + b2 Solving 120 = 10b + b2 Solving for variable 'b'. Reorder the terms: 120 + -10b + -1b2 = 10b + -10b + b2 + -1b2 Combine like terms: 10b + -10b = 0 120 + -10b + -1b2 = 0 + b2 + -1b2 120 + -10b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 120 + -10b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + 10b + b2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 10b + 120 + b2 = 0 + 120 Reorder the terms: -120 + 120 + 10b + b2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 10b + b2 = 0 + 120 10b + b2 = 0 + 120 Combine like terms: 0 + 120 = 120 10b + b2 = 120 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = 120 + 25 Reorder the terms: 25 + 10b + b2 = 120 + 25 Combine like terms: 120 + 25 = 145 25 + 10b + b2 = 145 Factor a perfect square on the left side: (b + 5)(b + 5) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (b + 5) equal to 12.041594579 and -12.041594579.Subproblem 1
b + 5 = 12.041594579 Simplifying b + 5 = 12.041594579 Reorder the terms: 5 + b = 12.041594579 Solving 5 + b = 12.041594579 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 12.041594579 + -5 Combine like terms: 5 + -5 = 0 0 + b = 12.041594579 + -5 b = 12.041594579 + -5 Combine like terms: 12.041594579 + -5 = 7.041594579 b = 7.041594579 Simplifying b = 7.041594579Subproblem 2
b + 5 = -12.041594579 Simplifying b + 5 = -12.041594579 Reorder the terms: 5 + b = -12.041594579 Solving 5 + b = -12.041594579 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -12.041594579 + -5 Combine like terms: 5 + -5 = 0 0 + b = -12.041594579 + -5 b = -12.041594579 + -5 Combine like terms: -12.041594579 + -5 = -17.041594579 b = -17.041594579 Simplifying b = -17.041594579Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.041594579, -17.041594579}
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