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Simplifying 12b2 + 93b + -8 = 0 Reorder the terms: -8 + 93b + 12b2 = 0 Solving -8 + 93b + 12b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + 7.75b + b2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 7.75b + 0.6666666667 + b2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 7.75b + b2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 7.75b + b2 = 0 + 0.6666666667 7.75b + b2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 7.75b + b2 = 0.6666666667 The b term is 7.75b. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75b + 15.015625 + b2 = 0.6666666667 + 15.015625 Reorder the terms: 15.015625 + 7.75b + b2 = 0.6666666667 + 15.015625 Combine like terms: 0.6666666667 + 15.015625 = 15.6822916667 15.015625 + 7.75b + b2 = 15.6822916667 Factor a perfect square on the left side: (b + 3.875)(b + 3.875) = 15.6822916667 Calculate the square root of the right side: 3.960087331 Break this problem into two subproblems by setting (b + 3.875) equal to 3.960087331 and -3.960087331.Subproblem 1
b + 3.875 = 3.960087331 Simplifying b + 3.875 = 3.960087331 Reorder the terms: 3.875 + b = 3.960087331 Solving 3.875 + b = 3.960087331 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + b = 3.960087331 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + b = 3.960087331 + -3.875 b = 3.960087331 + -3.875 Combine like terms: 3.960087331 + -3.875 = 0.085087331 b = 0.085087331 Simplifying b = 0.085087331Subproblem 2
b + 3.875 = -3.960087331 Simplifying b + 3.875 = -3.960087331 Reorder the terms: 3.875 + b = -3.960087331 Solving 3.875 + b = -3.960087331 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + b = -3.960087331 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + b = -3.960087331 + -3.875 b = -3.960087331 + -3.875 Combine like terms: -3.960087331 + -3.875 = -7.835087331 b = -7.835087331 Simplifying b = -7.835087331Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.085087331, -7.835087331}
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