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Simplifying 80 + 22b + b2 = 0 Solving 80 + 22b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 22b + -80 + b2 = 0 + -80 Reorder the terms: 80 + -80 + 22b + b2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 22b + b2 = 0 + -80 22b + b2 = 0 + -80 Combine like terms: 0 + -80 = -80 22b + b2 = -80 The b term is 22b. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22b + 121 + b2 = -80 + 121 Reorder the terms: 121 + 22b + b2 = -80 + 121 Combine like terms: -80 + 121 = 41 121 + 22b + b2 = 41 Factor a perfect square on the left side: (b + 11)(b + 11) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (b + 11) equal to 6.403124237 and -6.403124237.Subproblem 1
b + 11 = 6.403124237 Simplifying b + 11 = 6.403124237 Reorder the terms: 11 + b = 6.403124237 Solving 11 + b = 6.403124237 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + b = 6.403124237 + -11 Combine like terms: 11 + -11 = 0 0 + b = 6.403124237 + -11 b = 6.403124237 + -11 Combine like terms: 6.403124237 + -11 = -4.596875763 b = -4.596875763 Simplifying b = -4.596875763Subproblem 2
b + 11 = -6.403124237 Simplifying b + 11 = -6.403124237 Reorder the terms: 11 + b = -6.403124237 Solving 11 + b = -6.403124237 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + b = -6.403124237 + -11 Combine like terms: 11 + -11 = 0 0 + b = -6.403124237 + -11 b = -6.403124237 + -11 Combine like terms: -6.403124237 + -11 = -17.403124237 b = -17.403124237 Simplifying b = -17.403124237Solution
The solution to the problem is based on the solutions from the subproblems. b = {-4.596875763, -17.403124237}
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