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Simplifying b2 + 6b + -62 = 0 Reorder the terms: -62 + 6b + b2 = 0 Solving -62 + 6b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 6b + 62 + b2 = 0 + 62 Reorder the terms: -62 + 62 + 6b + b2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 6b + b2 = 0 + 62 6b + b2 = 0 + 62 Combine like terms: 0 + 62 = 62 6b + b2 = 62 The b term is 6b. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6b + 9 + b2 = 62 + 9 Reorder the terms: 9 + 6b + b2 = 62 + 9 Combine like terms: 62 + 9 = 71 9 + 6b + b2 = 71 Factor a perfect square on the left side: (b + 3)(b + 3) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (b + 3) equal to 8.426149773 and -8.426149773.Subproblem 1
b + 3 = 8.426149773 Simplifying b + 3 = 8.426149773 Reorder the terms: 3 + b = 8.426149773 Solving 3 + b = 8.426149773 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 8.426149773 + -3 Combine like terms: 3 + -3 = 0 0 + b = 8.426149773 + -3 b = 8.426149773 + -3 Combine like terms: 8.426149773 + -3 = 5.426149773 b = 5.426149773 Simplifying b = 5.426149773Subproblem 2
b + 3 = -8.426149773 Simplifying b + 3 = -8.426149773 Reorder the terms: 3 + b = -8.426149773 Solving 3 + b = -8.426149773 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = -8.426149773 + -3 Combine like terms: 3 + -3 = 0 0 + b = -8.426149773 + -3 b = -8.426149773 + -3 Combine like terms: -8.426149773 + -3 = -11.426149773 b = -11.426149773 Simplifying b = -11.426149773Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.426149773, -11.426149773}
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