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Simplifying -1b * -1b + 6b + 7 = 0 Reorder the terms for easier multiplication: -1 * -1b * b + 6b + 7 = 0 Multiply -1 * -1 1b * b + 6b + 7 = 0 Multiply b * b 1b2 + 6b + 7 = 0 Reorder the terms: 7 + 6b + 1b2 = 0 Solving 7 + 6b + 1b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6b + -7 + b2 = 0 + -7 Reorder the terms: 7 + -7 + 6b + b2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6b + b2 = 0 + -7 6b + b2 = 0 + -7 Combine like terms: 0 + -7 = -7 6b + b2 = -7 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 = -7 + 9 Reorder the terms: 9 + 6b + b2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6b + b2 = 2 Factor a perfect square on the left side: (b + 3)(b + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (b + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
b + 3 = 1.414213562 Simplifying b + 3 = 1.414213562 Reorder the terms: 3 + b = 1.414213562 Solving 3 + b = 1.414213562 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 = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + b = 1.414213562 + -3 b = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 b = -1.585786438 Simplifying b = -1.585786438Subproblem 2
b + 3 = -1.414213562 Simplifying b + 3 = -1.414213562 Reorder the terms: 3 + b = -1.414213562 Solving 3 + b = -1.414213562 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 = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + b = -1.414213562 + -3 b = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 b = -4.414213562 Simplifying b = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.585786438, -4.414213562}
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