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Simplifying -10b + -1b2 = 10 Solving -10b + -1b2 = 10 Solving for variable 'b'. Reorder the terms: -10 + -10b + -1b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -10b + -1b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 10b + b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 10b + b2)' equal to zero and attempt to solve: Simplifying 10 + 10b + b2 = 0 Solving 10 + 10b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 10b + -10 + b2 = 0 + -10 Reorder the terms: 10 + -10 + 10b + b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 10b + b2 = 0 + -10 10b + b2 = 0 + -10 Combine like terms: 0 + -10 = -10 10b + b2 = -10 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = -10 + 25 Reorder the terms: 25 + 10b + b2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + 10b + b2 = 15 Factor a perfect square on the left side: (b + 5)(b + 5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (b + 5) equal to 3.872983346 and -3.872983346.Subproblem 1
b + 5 = 3.872983346 Simplifying b + 5 = 3.872983346 Reorder the terms: 5 + b = 3.872983346 Solving 5 + b = 3.872983346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + b = 3.872983346 + -5 b = 3.872983346 + -5 Combine like terms: 3.872983346 + -5 = -1.127016654 b = -1.127016654 Simplifying b = -1.127016654Subproblem 2
b + 5 = -3.872983346 Simplifying b + 5 = -3.872983346 Reorder the terms: 5 + b = -3.872983346 Solving 5 + b = -3.872983346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + b = -3.872983346 + -5 b = -3.872983346 + -5 Combine like terms: -3.872983346 + -5 = -8.872983346 b = -8.872983346 Simplifying b = -8.872983346Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.127016654, -8.872983346}Solution
b = {-1.127016654, -8.872983346}
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