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Simplifying 800b + -1b2 = 1000 Solving 800b + -1b2 = 1000 Solving for variable 'b'. Reorder the terms: -1000 + 800b + -1b2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 800b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1000 + -800b + b2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -800b + -1000 + b2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -800b + b2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -800b + b2 = 0 + -1000 -800b + b2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -800b + b2 = -1000 The b term is -800b. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800b + 160000 + b2 = -1000 + 160000 Reorder the terms: 160000 + -800b + b2 = -1000 + 160000 Combine like terms: -1000 + 160000 = 159000 160000 + -800b + b2 = 159000 Factor a perfect square on the left side: (b + -400)(b + -400) = 159000 Calculate the square root of the right side: 398.748040748 Break this problem into two subproblems by setting (b + -400) equal to 398.748040748 and -398.748040748.Subproblem 1
b + -400 = 398.748040748 Simplifying b + -400 = 398.748040748 Reorder the terms: -400 + b = 398.748040748 Solving -400 + b = 398.748040748 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + b = 398.748040748 + 400 Combine like terms: -400 + 400 = 0 0 + b = 398.748040748 + 400 b = 398.748040748 + 400 Combine like terms: 398.748040748 + 400 = 798.748040748 b = 798.748040748 Simplifying b = 798.748040748Subproblem 2
b + -400 = -398.748040748 Simplifying b + -400 = -398.748040748 Reorder the terms: -400 + b = -398.748040748 Solving -400 + b = -398.748040748 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + b = -398.748040748 + 400 Combine like terms: -400 + 400 = 0 0 + b = -398.748040748 + 400 b = -398.748040748 + 400 Combine like terms: -398.748040748 + 400 = 1.251959252 b = 1.251959252 Simplifying b = 1.251959252Solution
The solution to the problem is based on the solutions from the subproblems. b = {798.748040748, 1.251959252}
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