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Simplifying b2 + 10b = 3 Reorder the terms: 10b + b2 = 3 Solving 10b + b2 = 3 Solving for variable 'b'. Reorder the terms: -3 + 10b + b2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 10b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 10b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + 10b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10b + b2 = 0 + 3 10b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 10b + b2 = 3 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 = 3 + 25 Reorder the terms: 25 + 10b + b2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + 10b + b2 = 28 Factor a perfect square on the left side: (b + 5)(b + 5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (b + 5) equal to 5.291502622 and -5.291502622.Subproblem 1
b + 5 = 5.291502622 Simplifying b + 5 = 5.291502622 Reorder the terms: 5 + b = 5.291502622 Solving 5 + b = 5.291502622 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 = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + b = 5.291502622 + -5 b = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 b = 0.291502622 Simplifying b = 0.291502622Subproblem 2
b + 5 = -5.291502622 Simplifying b + 5 = -5.291502622 Reorder the terms: 5 + b = -5.291502622 Solving 5 + b = -5.291502622 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 = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + b = -5.291502622 + -5 b = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 b = -10.291502622 Simplifying b = -10.291502622Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.291502622, -10.291502622}
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