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Simplifying -7(-9b + -6) + 3b + 2b2 + 1 = 0 Reorder the terms: -7(-6 + -9b) + 3b + 2b2 + 1 = 0 (-6 * -7 + -9b * -7) + 3b + 2b2 + 1 = 0 (42 + 63b) + 3b + 2b2 + 1 = 0 Reorder the terms: 42 + 1 + 63b + 3b + 2b2 = 0 Combine like terms: 42 + 1 = 43 43 + 63b + 3b + 2b2 = 0 Combine like terms: 63b + 3b = 66b 43 + 66b + 2b2 = 0 Solving 43 + 66b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 21.5 + 33b + b2 = 0 Move the constant term to the right: Add '-21.5' to each side of the equation. 21.5 + 33b + -21.5 + b2 = 0 + -21.5 Reorder the terms: 21.5 + -21.5 + 33b + b2 = 0 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + 33b + b2 = 0 + -21.5 33b + b2 = 0 + -21.5 Combine like terms: 0 + -21.5 = -21.5 33b + b2 = -21.5 The b term is 33b. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33b + 272.25 + b2 = -21.5 + 272.25 Reorder the terms: 272.25 + 33b + b2 = -21.5 + 272.25 Combine like terms: -21.5 + 272.25 = 250.75 272.25 + 33b + b2 = 250.75 Factor a perfect square on the left side: (b + 16.5)(b + 16.5) = 250.75 Calculate the square root of the right side: 15.835087622 Break this problem into two subproblems by setting (b + 16.5) equal to 15.835087622 and -15.835087622.Subproblem 1
b + 16.5 = 15.835087622 Simplifying b + 16.5 = 15.835087622 Reorder the terms: 16.5 + b = 15.835087622 Solving 16.5 + b = 15.835087622 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + b = 15.835087622 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + b = 15.835087622 + -16.5 b = 15.835087622 + -16.5 Combine like terms: 15.835087622 + -16.5 = -0.664912378 b = -0.664912378 Simplifying b = -0.664912378Subproblem 2
b + 16.5 = -15.835087622 Simplifying b + 16.5 = -15.835087622 Reorder the terms: 16.5 + b = -15.835087622 Solving 16.5 + b = -15.835087622 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + b = -15.835087622 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + b = -15.835087622 + -16.5 b = -15.835087622 + -16.5 Combine like terms: -15.835087622 + -16.5 = -32.335087622 b = -32.335087622 Simplifying b = -32.335087622Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.664912378, -32.335087622}
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