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Simplifying b(5 + b) = 88 (5 * b + b * b) = 88 (5b + b2) = 88 Solving 5b + b2 = 88 Solving for variable 'b'. Reorder the terms: -88 + 5b + b2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 5b + 88 + b2 = 0 + 88 Reorder the terms: -88 + 88 + 5b + b2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 5b + b2 = 0 + 88 5b + b2 = 0 + 88 Combine like terms: 0 + 88 = 88 5b + b2 = 88 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = 88 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 88 + 6.25 Combine like terms: 88 + 6.25 = 94.25 6.25 + 5b + b2 = 94.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (b + 2.5) equal to 9.708243919 and -9.708243919.Subproblem 1
b + 2.5 = 9.708243919 Simplifying b + 2.5 = 9.708243919 Reorder the terms: 2.5 + b = 9.708243919 Solving 2.5 + b = 9.708243919 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 9.708243919 + -2.5 b = 9.708243919 + -2.5 Combine like terms: 9.708243919 + -2.5 = 7.208243919 b = 7.208243919 Simplifying b = 7.208243919Subproblem 2
b + 2.5 = -9.708243919 Simplifying b + 2.5 = -9.708243919 Reorder the terms: 2.5 + b = -9.708243919 Solving 2.5 + b = -9.708243919 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -9.708243919 + -2.5 b = -9.708243919 + -2.5 Combine like terms: -9.708243919 + -2.5 = -12.208243919 b = -12.208243919 Simplifying b = -12.208243919Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.208243919, -12.208243919}
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