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Simplifying 7b + 0.5b2 = 120 Solving 7b + 0.5b2 = 120 Solving for variable 'b'. Reorder the terms: -120 + 7b + 0.5b2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 7b + 0.5b2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -240 + 14b + b2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + 14b + 240 + b2 = 0 + 240 Reorder the terms: -240 + 240 + 14b + b2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 14b + b2 = 0 + 240 14b + b2 = 0 + 240 Combine like terms: 0 + 240 = 240 14b + b2 = 240 The b term is 14b. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14b + 49 + b2 = 240 + 49 Reorder the terms: 49 + 14b + b2 = 240 + 49 Combine like terms: 240 + 49 = 289 49 + 14b + b2 = 289 Factor a perfect square on the left side: (b + 7)(b + 7) = 289 Calculate the square root of the right side: 17 Break this problem into two subproblems by setting (b + 7) equal to 17 and -17.Subproblem 1
b + 7 = 17 Simplifying b + 7 = 17 Reorder the terms: 7 + b = 17 Solving 7 + b = 17 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = 17 + -7 Combine like terms: 7 + -7 = 0 0 + b = 17 + -7 b = 17 + -7 Combine like terms: 17 + -7 = 10 b = 10 Simplifying b = 10Subproblem 2
b + 7 = -17 Simplifying b + 7 = -17 Reorder the terms: 7 + b = -17 Solving 7 + b = -17 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = -17 + -7 Combine like terms: 7 + -7 = 0 0 + b = -17 + -7 b = -17 + -7 Combine like terms: -17 + -7 = -24 b = -24 Simplifying b = -24Solution
The solution to the problem is based on the solutions from the subproblems. b = {10, -24}
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