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Simplifying -2 + -9b = 5b2 Solving -2 + -9b = 5b2 Solving for variable 'b'. Combine like terms: 5b2 + -5b2 = 0 -2 + -9b + -5b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 9b + 5b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 9b + 5b2)' equal to zero and attempt to solve: Simplifying 2 + 9b + 5b2 = 0 Solving 2 + 9b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.8b + b2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.8b + -0.4 + b2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.8b + b2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.8b + b2 = 0 + -0.4 1.8b + b2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.8b + b2 = -0.4 The b term is 1.8b. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8b + 0.81 + b2 = -0.4 + 0.81 Reorder the terms: 0.81 + 1.8b + b2 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + 1.8b + b2 = 0.41 Factor a perfect square on the left side: (b + 0.9)(b + 0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (b + 0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
b + 0.9 = 0.640312424 Simplifying b + 0.9 = 0.640312424 Reorder the terms: 0.9 + b = 0.640312424 Solving 0.9 + b = 0.640312424 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + b = 0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + b = 0.640312424 + -0.9 b = 0.640312424 + -0.9 Combine like terms: 0.640312424 + -0.9 = -0.259687576 b = -0.259687576 Simplifying b = -0.259687576Subproblem 2
b + 0.9 = -0.640312424 Simplifying b + 0.9 = -0.640312424 Reorder the terms: 0.9 + b = -0.640312424 Solving 0.9 + b = -0.640312424 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + b = -0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + b = -0.640312424 + -0.9 b = -0.640312424 + -0.9 Combine like terms: -0.640312424 + -0.9 = -1.540312424 b = -1.540312424 Simplifying b = -1.540312424Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.259687576, -1.540312424}Solution
b = {-0.259687576, -1.540312424}
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