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Simplifying b2 + 22b + -16 = 0 Reorder the terms: -16 + 22b + b2 = 0 Solving -16 + 22b + 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 + 22b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + 22b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 22b + b2 = 0 + 16 22b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 22b + b2 = 16 The b term is 22b. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22b + 121 + b2 = 16 + 121 Reorder the terms: 121 + 22b + b2 = 16 + 121 Combine like terms: 16 + 121 = 137 121 + 22b + b2 = 137 Factor a perfect square on the left side: (b + 11)(b + 11) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (b + 11) equal to 11.704699911 and -11.704699911.Subproblem 1
b + 11 = 11.704699911 Simplifying b + 11 = 11.704699911 Reorder the terms: 11 + b = 11.704699911 Solving 11 + b = 11.704699911 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + b = 11.704699911 + -11 Combine like terms: 11 + -11 = 0 0 + b = 11.704699911 + -11 b = 11.704699911 + -11 Combine like terms: 11.704699911 + -11 = 0.704699911 b = 0.704699911 Simplifying b = 0.704699911Subproblem 2
b + 11 = -11.704699911 Simplifying b + 11 = -11.704699911 Reorder the terms: 11 + b = -11.704699911 Solving 11 + b = -11.704699911 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + b = -11.704699911 + -11 Combine like terms: 11 + -11 = 0 0 + b = -11.704699911 + -11 b = -11.704699911 + -11 Combine like terms: -11.704699911 + -11 = -22.704699911 b = -22.704699911 Simplifying b = -22.704699911Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.704699911, -22.704699911}
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