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Simplifying b2 + 5b + -64 = 0 Reorder the terms: -64 + 5b + b2 = 0 Solving -64 + 5b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 5b + 64 + b2 = 0 + 64 Reorder the terms: -64 + 64 + 5b + b2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 5b + b2 = 0 + 64 5b + b2 = 0 + 64 Combine like terms: 0 + 64 = 64 5b + b2 = 64 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 = 64 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 64 + 6.25 Combine like terms: 64 + 6.25 = 70.25 6.25 + 5b + b2 = 70.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (b + 2.5) equal to 8.381527307 and -8.381527307.Subproblem 1
b + 2.5 = 8.381527307 Simplifying b + 2.5 = 8.381527307 Reorder the terms: 2.5 + b = 8.381527307 Solving 2.5 + b = 8.381527307 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 = 8.381527307 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 8.381527307 + -2.5 b = 8.381527307 + -2.5 Combine like terms: 8.381527307 + -2.5 = 5.881527307 b = 5.881527307 Simplifying b = 5.881527307Subproblem 2
b + 2.5 = -8.381527307 Simplifying b + 2.5 = -8.381527307 Reorder the terms: 2.5 + b = -8.381527307 Solving 2.5 + b = -8.381527307 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 = -8.381527307 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -8.381527307 + -2.5 b = -8.381527307 + -2.5 Combine like terms: -8.381527307 + -2.5 = -10.881527307 b = -10.881527307 Simplifying b = -10.881527307Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.881527307, -10.881527307}
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