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Simplifying 9b2 + 6b + 1 = 930 Reorder the terms: 1 + 6b + 9b2 = 930 Solving 1 + 6b + 9b2 = 930 Solving for variable 'b'. Reorder the terms: 1 + -930 + 6b + 9b2 = 930 + -930 Combine like terms: 1 + -930 = -929 -929 + 6b + 9b2 = 930 + -930 Combine like terms: 930 + -930 = 0 -929 + 6b + 9b2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -103.2222222 + 0.6666666667b + b2 = 0 Move the constant term to the right: Add '103.2222222' to each side of the equation. -103.2222222 + 0.6666666667b + 103.2222222 + b2 = 0 + 103.2222222 Reorder the terms: -103.2222222 + 103.2222222 + 0.6666666667b + b2 = 0 + 103.2222222 Combine like terms: -103.2222222 + 103.2222222 = 0.0000000 0.0000000 + 0.6666666667b + b2 = 0 + 103.2222222 0.6666666667b + b2 = 0 + 103.2222222 Combine like terms: 0 + 103.2222222 = 103.2222222 0.6666666667b + b2 = 103.2222222 The b term is 0.6666666667b. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667b + 0.1111111112 + b2 = 103.2222222 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667b + b2 = 103.2222222 + 0.1111111112 Combine like terms: 103.2222222 + 0.1111111112 = 103.3333333112 0.1111111112 + 0.6666666667b + b2 = 103.3333333112 Factor a perfect square on the left side: (b + 0.3333333334)(b + 0.3333333334) = 103.3333333112 Calculate the square root of the right side: 10.165300454 Break this problem into two subproblems by setting (b + 0.3333333334) equal to 10.165300454 and -10.165300454.Subproblem 1
b + 0.3333333334 = 10.165300454 Simplifying b + 0.3333333334 = 10.165300454 Reorder the terms: 0.3333333334 + b = 10.165300454 Solving 0.3333333334 + b = 10.165300454 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + b = 10.165300454 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + b = 10.165300454 + -0.3333333334 b = 10.165300454 + -0.3333333334 Combine like terms: 10.165300454 + -0.3333333334 = 9.8319671206 b = 9.8319671206 Simplifying b = 9.8319671206Subproblem 2
b + 0.3333333334 = -10.165300454 Simplifying b + 0.3333333334 = -10.165300454 Reorder the terms: 0.3333333334 + b = -10.165300454 Solving 0.3333333334 + b = -10.165300454 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + b = -10.165300454 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + b = -10.165300454 + -0.3333333334 b = -10.165300454 + -0.3333333334 Combine like terms: -10.165300454 + -0.3333333334 = -10.4986337874 b = -10.4986337874 Simplifying b = -10.4986337874Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.8319671206, -10.4986337874}
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