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Simplifying b2 + 6b + -56 = 0 Reorder the terms: -56 + 6b + b2 = 0 Solving -56 + 6b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 6b + 56 + b2 = 0 + 56 Reorder the terms: -56 + 56 + 6b + b2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 6b + b2 = 0 + 56 6b + b2 = 0 + 56 Combine like terms: 0 + 56 = 56 6b + b2 = 56 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 = 56 + 9 Reorder the terms: 9 + 6b + b2 = 56 + 9 Combine like terms: 56 + 9 = 65 9 + 6b + b2 = 65 Factor a perfect square on the left side: (b + 3)(b + 3) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (b + 3) equal to 8.062257748 and -8.062257748.Subproblem 1
b + 3 = 8.062257748 Simplifying b + 3 = 8.062257748 Reorder the terms: 3 + b = 8.062257748 Solving 3 + b = 8.062257748 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 = 8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + b = 8.062257748 + -3 b = 8.062257748 + -3 Combine like terms: 8.062257748 + -3 = 5.062257748 b = 5.062257748 Simplifying b = 5.062257748Subproblem 2
b + 3 = -8.062257748 Simplifying b + 3 = -8.062257748 Reorder the terms: 3 + b = -8.062257748 Solving 3 + b = -8.062257748 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 = -8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + b = -8.062257748 + -3 b = -8.062257748 + -3 Combine like terms: -8.062257748 + -3 = -11.062257748 b = -11.062257748 Simplifying b = -11.062257748Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.062257748, -11.062257748}
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