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Simplifying 81b2 + 99b + 25 = 0 Reorder the terms: 25 + 99b + 81b2 = 0 Solving 25 + 99b + 81b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.3086419753 + 1.222222222b + b2 = 0 Move the constant term to the right: Add '-0.3086419753' to each side of the equation. 0.3086419753 + 1.222222222b + -0.3086419753 + b2 = 0 + -0.3086419753 Reorder the terms: 0.3086419753 + -0.3086419753 + 1.222222222b + b2 = 0 + -0.3086419753 Combine like terms: 0.3086419753 + -0.3086419753 = 0.0000000000 0.0000000000 + 1.222222222b + b2 = 0 + -0.3086419753 1.222222222b + b2 = 0 + -0.3086419753 Combine like terms: 0 + -0.3086419753 = -0.3086419753 1.222222222b + b2 = -0.3086419753 The b term is 1.222222222b. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222b + 0.3734567900 + b2 = -0.3086419753 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222b + b2 = -0.3086419753 + 0.3734567900 Combine like terms: -0.3086419753 + 0.3734567900 = 0.0648148147 0.3734567900 + 1.222222222b + b2 = 0.0648148147 Factor a perfect square on the left side: (b + 0.611111111)(b + 0.611111111) = 0.0648148147 Calculate the square root of the right side: 0.254587538 Break this problem into two subproblems by setting (b + 0.611111111) equal to 0.254587538 and -0.254587538.Subproblem 1
b + 0.611111111 = 0.254587538 Simplifying b + 0.611111111 = 0.254587538 Reorder the terms: 0.611111111 + b = 0.254587538 Solving 0.611111111 + b = 0.254587538 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + b = 0.254587538 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + b = 0.254587538 + -0.611111111 b = 0.254587538 + -0.611111111 Combine like terms: 0.254587538 + -0.611111111 = -0.356523573 b = -0.356523573 Simplifying b = -0.356523573Subproblem 2
b + 0.611111111 = -0.254587538 Simplifying b + 0.611111111 = -0.254587538 Reorder the terms: 0.611111111 + b = -0.254587538 Solving 0.611111111 + b = -0.254587538 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + b = -0.254587538 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + b = -0.254587538 + -0.611111111 b = -0.254587538 + -0.611111111 Combine like terms: -0.254587538 + -0.611111111 = -0.865698649 b = -0.865698649 Simplifying b = -0.865698649Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.356523573, -0.865698649}
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