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Simplifying 100b + -1b2 = 200 Solving 100b + -1b2 = 200 Solving for variable 'b'. Reorder the terms: -200 + 100b + -1b2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 100b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 200 + -100b + b2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -100b + -200 + b2 = 0 + -200 Reorder the terms: 200 + -200 + -100b + b2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -100b + b2 = 0 + -200 -100b + b2 = 0 + -200 Combine like terms: 0 + -200 = -200 -100b + b2 = -200 The b term is -100b. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100b + 2500 + b2 = -200 + 2500 Reorder the terms: 2500 + -100b + b2 = -200 + 2500 Combine like terms: -200 + 2500 = 2300 2500 + -100b + b2 = 2300 Factor a perfect square on the left side: (b + -50)(b + -50) = 2300 Calculate the square root of the right side: 47.958315233 Break this problem into two subproblems by setting (b + -50) equal to 47.958315233 and -47.958315233.Subproblem 1
b + -50 = 47.958315233 Simplifying b + -50 = 47.958315233 Reorder the terms: -50 + b = 47.958315233 Solving -50 + b = 47.958315233 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + b = 47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + b = 47.958315233 + 50 b = 47.958315233 + 50 Combine like terms: 47.958315233 + 50 = 97.958315233 b = 97.958315233 Simplifying b = 97.958315233Subproblem 2
b + -50 = -47.958315233 Simplifying b + -50 = -47.958315233 Reorder the terms: -50 + b = -47.958315233 Solving -50 + b = -47.958315233 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + b = -47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + b = -47.958315233 + 50 b = -47.958315233 + 50 Combine like terms: -47.958315233 + 50 = 2.041684767 b = 2.041684767 Simplifying b = 2.041684767Solution
The solution to the problem is based on the solutions from the subproblems. b = {97.958315233, 2.041684767}
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