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Simplifying 25b + 11 = -1b2 Reorder the terms: 11 + 25b = -1b2 Solving 11 + 25b = -1b2 Solving for variable 'b'. Combine like terms: -1b2 + b2 = 0 11 + 25b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 25b + -11 + b2 = 0 + -11 Reorder the terms: 11 + -11 + 25b + b2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 25b + b2 = 0 + -11 25b + b2 = 0 + -11 Combine like terms: 0 + -11 = -11 25b + b2 = -11 The b term is 25b. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25b + 156.25 + b2 = -11 + 156.25 Reorder the terms: 156.25 + 25b + b2 = -11 + 156.25 Combine like terms: -11 + 156.25 = 145.25 156.25 + 25b + b2 = 145.25 Factor a perfect square on the left side: (b + 12.5)(b + 12.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (b + 12.5) equal to 12.051970793 and -12.051970793.Subproblem 1
b + 12.5 = 12.051970793 Simplifying b + 12.5 = 12.051970793 Reorder the terms: 12.5 + b = 12.051970793 Solving 12.5 + b = 12.051970793 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + b = 12.051970793 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + b = 12.051970793 + -12.5 b = 12.051970793 + -12.5 Combine like terms: 12.051970793 + -12.5 = -0.448029207 b = -0.448029207 Simplifying b = -0.448029207Subproblem 2
b + 12.5 = -12.051970793 Simplifying b + 12.5 = -12.051970793 Reorder the terms: 12.5 + b = -12.051970793 Solving 12.5 + b = -12.051970793 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + b = -12.051970793 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + b = -12.051970793 + -12.5 b = -12.051970793 + -12.5 Combine like terms: -12.051970793 + -12.5 = -24.551970793 b = -24.551970793 Simplifying b = -24.551970793Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.448029207, -24.551970793}
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