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Simplifying -15b2 + 17b + 6 = 0 Reorder the terms: 6 + 17b + -15b2 = 0 Solving 6 + 17b + -15b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.4 + -1.133333333b + b2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.133333333b + 0.4 + b2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.133333333b + b2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.133333333b + b2 = 0 + 0.4 -1.133333333b + b2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.133333333b + b2 = 0.4 The b term is -1.133333333b. Take half its coefficient (-0.5666666665). Square it (0.3211111109) and add it to both sides. Add '0.3211111109' to each side of the equation. -1.133333333b + 0.3211111109 + b2 = 0.4 + 0.3211111109 Reorder the terms: 0.3211111109 + -1.133333333b + b2 = 0.4 + 0.3211111109 Combine like terms: 0.4 + 0.3211111109 = 0.7211111109 0.3211111109 + -1.133333333b + b2 = 0.7211111109 Factor a perfect square on the left side: (b + -0.5666666665)(b + -0.5666666665) = 0.7211111109 Calculate the square root of the right side: 0.849182613 Break this problem into two subproblems by setting (b + -0.5666666665) equal to 0.849182613 and -0.849182613.Subproblem 1
b + -0.5666666665 = 0.849182613 Simplifying b + -0.5666666665 = 0.849182613 Reorder the terms: -0.5666666665 + b = 0.849182613 Solving -0.5666666665 + b = 0.849182613 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5666666665' to each side of the equation. -0.5666666665 + 0.5666666665 + b = 0.849182613 + 0.5666666665 Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000 0.0000000000 + b = 0.849182613 + 0.5666666665 b = 0.849182613 + 0.5666666665 Combine like terms: 0.849182613 + 0.5666666665 = 1.4158492795 b = 1.4158492795 Simplifying b = 1.4158492795Subproblem 2
b + -0.5666666665 = -0.849182613 Simplifying b + -0.5666666665 = -0.849182613 Reorder the terms: -0.5666666665 + b = -0.849182613 Solving -0.5666666665 + b = -0.849182613 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5666666665' to each side of the equation. -0.5666666665 + 0.5666666665 + b = -0.849182613 + 0.5666666665 Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000 0.0000000000 + b = -0.849182613 + 0.5666666665 b = -0.849182613 + 0.5666666665 Combine like terms: -0.849182613 + 0.5666666665 = -0.2825159465 b = -0.2825159465 Simplifying b = -0.2825159465Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.4158492795, -0.2825159465}
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