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Simplifying b2 + 20b + -54 = 0 Reorder the terms: -54 + 20b + b2 = 0 Solving -54 + 20b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 20b + 54 + b2 = 0 + 54 Reorder the terms: -54 + 54 + 20b + b2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 20b + b2 = 0 + 54 20b + b2 = 0 + 54 Combine like terms: 0 + 54 = 54 20b + b2 = 54 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 = 54 + 100 Reorder the terms: 100 + 20b + b2 = 54 + 100 Combine like terms: 54 + 100 = 154 100 + 20b + b2 = 154 Factor a perfect square on the left side: (b + 10)(b + 10) = 154 Calculate the square root of the right side: 12.409673646 Break this problem into two subproblems by setting (b + 10) equal to 12.409673646 and -12.409673646.Subproblem 1
b + 10 = 12.409673646 Simplifying b + 10 = 12.409673646 Reorder the terms: 10 + b = 12.409673646 Solving 10 + b = 12.409673646 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 = 12.409673646 + -10 Combine like terms: 10 + -10 = 0 0 + b = 12.409673646 + -10 b = 12.409673646 + -10 Combine like terms: 12.409673646 + -10 = 2.409673646 b = 2.409673646 Simplifying b = 2.409673646Subproblem 2
b + 10 = -12.409673646 Simplifying b + 10 = -12.409673646 Reorder the terms: 10 + b = -12.409673646 Solving 10 + b = -12.409673646 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 = -12.409673646 + -10 Combine like terms: 10 + -10 = 0 0 + b = -12.409673646 + -10 b = -12.409673646 + -10 Combine like terms: -12.409673646 + -10 = -22.409673646 b = -22.409673646 Simplifying b = -22.409673646Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.409673646, -22.409673646}
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