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Simplifying 17b2 + -21 = 7b + -1b Reorder the terms: -21 + 17b2 = 7b + -1b Combine like terms: 7b + -1b = 6b -21 + 17b2 = 6b Solving -21 + 17b2 = 6b Solving for variable 'b'. Reorder the terms: -21 + -6b + 17b2 = 6b + -6b Combine like terms: 6b + -6b = 0 -21 + -6b + 17b2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -1.235294118 + -0.3529411765b + b2 = 0 Move the constant term to the right: Add '1.235294118' to each side of the equation. -1.235294118 + -0.3529411765b + 1.235294118 + b2 = 0 + 1.235294118 Reorder the terms: -1.235294118 + 1.235294118 + -0.3529411765b + b2 = 0 + 1.235294118 Combine like terms: -1.235294118 + 1.235294118 = 0.000000000 0.000000000 + -0.3529411765b + b2 = 0 + 1.235294118 -0.3529411765b + b2 = 0 + 1.235294118 Combine like terms: 0 + 1.235294118 = 1.235294118 -0.3529411765b + b2 = 1.235294118 The b term is -0.3529411765b. Take half its coefficient (-0.1764705883). Square it (0.03114186853) and add it to both sides. Add '0.03114186853' to each side of the equation. -0.3529411765b + 0.03114186853 + b2 = 1.235294118 + 0.03114186853 Reorder the terms: 0.03114186853 + -0.3529411765b + b2 = 1.235294118 + 0.03114186853 Combine like terms: 1.235294118 + 0.03114186853 = 1.26643598653 0.03114186853 + -0.3529411765b + b2 = 1.26643598653 Factor a perfect square on the left side: (b + -0.1764705883)(b + -0.1764705883) = 1.26643598653 Calculate the square root of the right side: 1.125360381 Break this problem into two subproblems by setting (b + -0.1764705883) equal to 1.125360381 and -1.125360381.Subproblem 1
b + -0.1764705883 = 1.125360381 Simplifying b + -0.1764705883 = 1.125360381 Reorder the terms: -0.1764705883 + b = 1.125360381 Solving -0.1764705883 + b = 1.125360381 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + b = 1.125360381 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + b = 1.125360381 + 0.1764705883 b = 1.125360381 + 0.1764705883 Combine like terms: 1.125360381 + 0.1764705883 = 1.3018309693 b = 1.3018309693 Simplifying b = 1.3018309693Subproblem 2
b + -0.1764705883 = -1.125360381 Simplifying b + -0.1764705883 = -1.125360381 Reorder the terms: -0.1764705883 + b = -1.125360381 Solving -0.1764705883 + b = -1.125360381 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + b = -1.125360381 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + b = -1.125360381 + 0.1764705883 b = -1.125360381 + 0.1764705883 Combine like terms: -1.125360381 + 0.1764705883 = -0.9488897927 b = -0.9488897927 Simplifying b = -0.9488897927Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.3018309693, -0.9488897927}
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