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Simplifying b2 + -14b + -2 = 0 Reorder the terms: -2 + -14b + b2 = 0 Solving -2 + -14b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -14b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -14b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -14b + b2 = 0 + 2 -14b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -14b + b2 = 2 The b term is -14b. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14b + 49 + b2 = 2 + 49 Reorder the terms: 49 + -14b + b2 = 2 + 49 Combine like terms: 2 + 49 = 51 49 + -14b + b2 = 51 Factor a perfect square on the left side: (b + -7)(b + -7) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (b + -7) equal to 7.141428429 and -7.141428429.Subproblem 1
b + -7 = 7.141428429 Simplifying b + -7 = 7.141428429 Reorder the terms: -7 + b = 7.141428429 Solving -7 + b = 7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + b = 7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + b = 7.141428429 + 7 b = 7.141428429 + 7 Combine like terms: 7.141428429 + 7 = 14.141428429 b = 14.141428429 Simplifying b = 14.141428429Subproblem 2
b + -7 = -7.141428429 Simplifying b + -7 = -7.141428429 Reorder the terms: -7 + b = -7.141428429 Solving -7 + b = -7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + b = -7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + b = -7.141428429 + 7 b = -7.141428429 + 7 Combine like terms: -7.141428429 + 7 = -0.141428429 b = -0.141428429 Simplifying b = -0.141428429Solution
The solution to the problem is based on the solutions from the subproblems. b = {14.141428429, -0.141428429}
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