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Simplifying b2 + -16 + -20b = 0 Reorder the terms: -16 + -20b + b2 = 0 Solving -16 + -20b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -20b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + -20b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -20b + b2 = 0 + 16 -20b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 -20b + b2 = 16 The b term is -20b. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20b + 100 + b2 = 16 + 100 Reorder the terms: 100 + -20b + b2 = 16 + 100 Combine like terms: 16 + 100 = 116 100 + -20b + b2 = 116 Factor a perfect square on the left side: (b + -10)(b + -10) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (b + -10) equal to 10.770329614 and -10.770329614.Subproblem 1
b + -10 = 10.770329614 Simplifying b + -10 = 10.770329614 Reorder the terms: -10 + b = 10.770329614 Solving -10 + b = 10.770329614 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + b = 10.770329614 + 10 Combine like terms: -10 + 10 = 0 0 + b = 10.770329614 + 10 b = 10.770329614 + 10 Combine like terms: 10.770329614 + 10 = 20.770329614 b = 20.770329614 Simplifying b = 20.770329614Subproblem 2
b + -10 = -10.770329614 Simplifying b + -10 = -10.770329614 Reorder the terms: -10 + b = -10.770329614 Solving -10 + b = -10.770329614 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + b = -10.770329614 + 10 Combine like terms: -10 + 10 = 0 0 + b = -10.770329614 + 10 b = -10.770329614 + 10 Combine like terms: -10.770329614 + 10 = -0.770329614 b = -0.770329614 Simplifying b = -0.770329614Solution
The solution to the problem is based on the solutions from the subproblems. b = {20.770329614, -0.770329614}
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