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Simplifying 11.2b + -1b2 = 10 Solving 11.2b + -1b2 = 10 Solving for variable 'b'. Reorder the terms: -10 + 11.2b + -1b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 11.2b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -11.2b + b2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -11.2b + -10 + b2 = 0 + -10 Reorder the terms: 10 + -10 + -11.2b + b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -11.2b + b2 = 0 + -10 -11.2b + b2 = 0 + -10 Combine like terms: 0 + -10 = -10 -11.2b + b2 = -10 The b term is -11.2b. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2b + 31.36 + b2 = -10 + 31.36 Reorder the terms: 31.36 + -11.2b + b2 = -10 + 31.36 Combine like terms: -10 + 31.36 = 21.36 31.36 + -11.2b + b2 = 21.36 Factor a perfect square on the left side: (b + -5.6)(b + -5.6) = 21.36 Calculate the square root of the right side: 4.621688003 Break this problem into two subproblems by setting (b + -5.6) equal to 4.621688003 and -4.621688003.Subproblem 1
b + -5.6 = 4.621688003 Simplifying b + -5.6 = 4.621688003 Reorder the terms: -5.6 + b = 4.621688003 Solving -5.6 + b = 4.621688003 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + b = 4.621688003 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + b = 4.621688003 + 5.6 b = 4.621688003 + 5.6 Combine like terms: 4.621688003 + 5.6 = 10.221688003 b = 10.221688003 Simplifying b = 10.221688003Subproblem 2
b + -5.6 = -4.621688003 Simplifying b + -5.6 = -4.621688003 Reorder the terms: -5.6 + b = -4.621688003 Solving -5.6 + b = -4.621688003 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + b = -4.621688003 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + b = -4.621688003 + 5.6 b = -4.621688003 + 5.6 Combine like terms: -4.621688003 + 5.6 = 0.978311997 b = 0.978311997 Simplifying b = 0.978311997Solution
The solution to the problem is based on the solutions from the subproblems. b = {10.221688003, 0.978311997}
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