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Simplifying b2 + -20b + -50 = 0 Reorder the terms: -50 + -20b + b2 = 0 Solving -50 + -20b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -20b + 50 + b2 = 0 + 50 Reorder the terms: -50 + 50 + -20b + b2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -20b + b2 = 0 + 50 -20b + b2 = 0 + 50 Combine like terms: 0 + 50 = 50 -20b + b2 = 50 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 = 50 + 100 Reorder the terms: 100 + -20b + b2 = 50 + 100 Combine like terms: 50 + 100 = 150 100 + -20b + b2 = 150 Factor a perfect square on the left side: (b + -10)(b + -10) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (b + -10) equal to 12.247448714 and -12.247448714.Subproblem 1
b + -10 = 12.247448714 Simplifying b + -10 = 12.247448714 Reorder the terms: -10 + b = 12.247448714 Solving -10 + b = 12.247448714 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 = 12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + b = 12.247448714 + 10 b = 12.247448714 + 10 Combine like terms: 12.247448714 + 10 = 22.247448714 b = 22.247448714 Simplifying b = 22.247448714Subproblem 2
b + -10 = -12.247448714 Simplifying b + -10 = -12.247448714 Reorder the terms: -10 + b = -12.247448714 Solving -10 + b = -12.247448714 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 = -12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + b = -12.247448714 + 10 b = -12.247448714 + 10 Combine like terms: -12.247448714 + 10 = -2.247448714 b = -2.247448714 Simplifying b = -2.247448714Solution
The solution to the problem is based on the solutions from the subproblems. b = {22.247448714, -2.247448714}
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