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Simplifying 8b2 + -7b + -7 = 0 Reorder the terms: -7 + -7b + 8b2 = 0 Solving -7 + -7b + 8b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.875b + b2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.875b + 0.875 + b2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.875b + b2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.875b + b2 = 0 + 0.875 -0.875b + b2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.875b + b2 = 0.875 The b term is -0.875b. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875b + 0.19140625 + b2 = 0.875 + 0.19140625 Reorder the terms: 0.19140625 + -0.875b + b2 = 0.875 + 0.19140625 Combine like terms: 0.875 + 0.19140625 = 1.06640625 0.19140625 + -0.875b + b2 = 1.06640625 Factor a perfect square on the left side: (b + -0.4375)(b + -0.4375) = 1.06640625 Calculate the square root of the right side: 1.032669478 Break this problem into two subproblems by setting (b + -0.4375) equal to 1.032669478 and -1.032669478.Subproblem 1
b + -0.4375 = 1.032669478 Simplifying b + -0.4375 = 1.032669478 Reorder the terms: -0.4375 + b = 1.032669478 Solving -0.4375 + b = 1.032669478 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + b = 1.032669478 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + b = 1.032669478 + 0.4375 b = 1.032669478 + 0.4375 Combine like terms: 1.032669478 + 0.4375 = 1.470169478 b = 1.470169478 Simplifying b = 1.470169478Subproblem 2
b + -0.4375 = -1.032669478 Simplifying b + -0.4375 = -1.032669478 Reorder the terms: -0.4375 + b = -1.032669478 Solving -0.4375 + b = -1.032669478 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + b = -1.032669478 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + b = -1.032669478 + 0.4375 b = -1.032669478 + 0.4375 Combine like terms: -1.032669478 + 0.4375 = -0.595169478 b = -0.595169478 Simplifying b = -0.595169478Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.470169478, -0.595169478}
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