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Simplifying 0.5b2 + -5b = 600 Reorder the terms: -5b + 0.5b2 = 600 Solving -5b + 0.5b2 = 600 Solving for variable 'b'. Reorder the terms: -600 + -5b + 0.5b2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + -5b + 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'. -1200 + -10b + b2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + -10b + 1200 + b2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -10b + b2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -10b + b2 = 0 + 1200 -10b + b2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -10b + b2 = 1200 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 = 1200 + 25 Reorder the terms: 25 + -10b + b2 = 1200 + 25 Combine like terms: 1200 + 25 = 1225 25 + -10b + b2 = 1225 Factor a perfect square on the left side: (b + -5)(b + -5) = 1225 Calculate the square root of the right side: 35 Break this problem into two subproblems by setting (b + -5) equal to 35 and -35.Subproblem 1
b + -5 = 35 Simplifying b + -5 = 35 Reorder the terms: -5 + b = 35 Solving -5 + b = 35 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 = 35 + 5 Combine like terms: -5 + 5 = 0 0 + b = 35 + 5 b = 35 + 5 Combine like terms: 35 + 5 = 40 b = 40 Simplifying b = 40Subproblem 2
b + -5 = -35 Simplifying b + -5 = -35 Reorder the terms: -5 + b = -35 Solving -5 + b = -35 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 = -35 + 5 Combine like terms: -5 + 5 = 0 0 + b = -35 + 5 b = -35 + 5 Combine like terms: -35 + 5 = -30 b = -30 Simplifying b = -30Solution
The solution to the problem is based on the solutions from the subproblems. b = {40, -30}
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