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Simplifying -1b2 + 8b = 10 Reorder the terms: 8b + -1b2 = 10 Solving 8b + -1b2 = 10 Solving for variable 'b'. Reorder the terms: -10 + 8b + -1b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 8b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -8b + b2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8b + -10 + b2 = 0 + -10 Reorder the terms: 10 + -10 + -8b + b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8b + b2 = 0 + -10 -8b + b2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8b + b2 = -10 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = -10 + 16 Reorder the terms: 16 + -8b + b2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8b + b2 = 6 Factor a perfect square on the left side: (b + -4)(b + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (b + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
b + -4 = 2.449489743 Simplifying b + -4 = 2.449489743 Reorder the terms: -4 + b = 2.449489743 Solving -4 + b = 2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + b = 2.449489743 + 4 b = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 b = 6.449489743 Simplifying b = 6.449489743Subproblem 2
b + -4 = -2.449489743 Simplifying b + -4 = -2.449489743 Reorder the terms: -4 + b = -2.449489743 Solving -4 + b = -2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + b = -2.449489743 + 4 b = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 b = 1.550510257 Simplifying b = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.449489743, 1.550510257}
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