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Simplifying 10b2 = 27b + -8 Reorder the terms: 10b2 = -8 + 27b Solving 10b2 = -8 + 27b Solving for variable 'b'. Reorder the terms: 8 + -27b + 10b2 = -8 + 27b + 8 + -27b Reorder the terms: 8 + -27b + 10b2 = -8 + 8 + 27b + -27b Combine like terms: -8 + 8 = 0 8 + -27b + 10b2 = 0 + 27b + -27b 8 + -27b + 10b2 = 27b + -27b Combine like terms: 27b + -27b = 0 8 + -27b + 10b2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.8 + -2.7b + b2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.7b + -0.8 + b2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.7b + b2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.7b + b2 = 0 + -0.8 -2.7b + b2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.7b + b2 = -0.8 The b term is -2.7b. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7b + 1.8225 + b2 = -0.8 + 1.8225 Reorder the terms: 1.8225 + -2.7b + b2 = -0.8 + 1.8225 Combine like terms: -0.8 + 1.8225 = 1.0225 1.8225 + -2.7b + b2 = 1.0225 Factor a perfect square on the left side: (b + -1.35)(b + -1.35) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (b + -1.35) equal to 1.011187421 and -1.011187421.Subproblem 1
b + -1.35 = 1.011187421 Simplifying b + -1.35 = 1.011187421 Reorder the terms: -1.35 + b = 1.011187421 Solving -1.35 + b = 1.011187421 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + b = 1.011187421 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + b = 1.011187421 + 1.35 b = 1.011187421 + 1.35 Combine like terms: 1.011187421 + 1.35 = 2.361187421 b = 2.361187421 Simplifying b = 2.361187421Subproblem 2
b + -1.35 = -1.011187421 Simplifying b + -1.35 = -1.011187421 Reorder the terms: -1.35 + b = -1.011187421 Solving -1.35 + b = -1.011187421 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + b = -1.011187421 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + b = -1.011187421 + 1.35 b = -1.011187421 + 1.35 Combine like terms: -1.011187421 + 1.35 = 0.338812579 b = 0.338812579 Simplifying b = 0.338812579Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.361187421, 0.338812579}
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