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Simplifying 7b2 + -14b + -55 = 0 Reorder the terms: -55 + -14b + 7b2 = 0 Solving -55 + -14b + 7b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7.857142857 + -2b + b2 = 0 Move the constant term to the right: Add '7.857142857' to each side of the equation. -7.857142857 + -2b + 7.857142857 + b2 = 0 + 7.857142857 Reorder the terms: -7.857142857 + 7.857142857 + -2b + b2 = 0 + 7.857142857 Combine like terms: -7.857142857 + 7.857142857 = 0.000000000 0.000000000 + -2b + b2 = 0 + 7.857142857 -2b + b2 = 0 + 7.857142857 Combine like terms: 0 + 7.857142857 = 7.857142857 -2b + b2 = 7.857142857 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 7.857142857 + 1 Reorder the terms: 1 + -2b + b2 = 7.857142857 + 1 Combine like terms: 7.857142857 + 1 = 8.857142857 1 + -2b + b2 = 8.857142857 Factor a perfect square on the left side: (b + -1)(b + -1) = 8.857142857 Calculate the square root of the right side: 2.976095237 Break this problem into two subproblems by setting (b + -1) equal to 2.976095237 and -2.976095237.Subproblem 1
b + -1 = 2.976095237 Simplifying b + -1 = 2.976095237 Reorder the terms: -1 + b = 2.976095237 Solving -1 + b = 2.976095237 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 2.976095237 + 1 Combine like terms: -1 + 1 = 0 0 + b = 2.976095237 + 1 b = 2.976095237 + 1 Combine like terms: 2.976095237 + 1 = 3.976095237 b = 3.976095237 Simplifying b = 3.976095237Subproblem 2
b + -1 = -2.976095237 Simplifying b + -1 = -2.976095237 Reorder the terms: -1 + b = -2.976095237 Solving -1 + b = -2.976095237 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -2.976095237 + 1 Combine like terms: -1 + 1 = 0 0 + b = -2.976095237 + 1 b = -2.976095237 + 1 Combine like terms: -2.976095237 + 1 = -1.976095237 b = -1.976095237 Simplifying b = -1.976095237Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.976095237, -1.976095237}
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