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Simplifying b2 + -12b + -14 = 0 Reorder the terms: -14 + -12b + b2 = 0 Solving -14 + -12b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -12b + 14 + b2 = 0 + 14 Reorder the terms: -14 + 14 + -12b + b2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -12b + b2 = 0 + 14 -12b + b2 = 0 + 14 Combine like terms: 0 + 14 = 14 -12b + b2 = 14 The b term is -12b. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12b + 36 + b2 = 14 + 36 Reorder the terms: 36 + -12b + b2 = 14 + 36 Combine like terms: 14 + 36 = 50 36 + -12b + b2 = 50 Factor a perfect square on the left side: (b + -6)(b + -6) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (b + -6) equal to 7.071067812 and -7.071067812.Subproblem 1
b + -6 = 7.071067812 Simplifying b + -6 = 7.071067812 Reorder the terms: -6 + b = 7.071067812 Solving -6 + b = 7.071067812 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + b = 7.071067812 + 6 b = 7.071067812 + 6 Combine like terms: 7.071067812 + 6 = 13.071067812 b = 13.071067812 Simplifying b = 13.071067812Subproblem 2
b + -6 = -7.071067812 Simplifying b + -6 = -7.071067812 Reorder the terms: -6 + b = -7.071067812 Solving -6 + b = -7.071067812 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + b = -7.071067812 + 6 b = -7.071067812 + 6 Combine like terms: -7.071067812 + 6 = -1.071067812 b = -1.071067812 Simplifying b = -1.071067812Solution
The solution to the problem is based on the solutions from the subproblems. b = {13.071067812, -1.071067812}
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