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Simplifying b2 + -4b + -40 = 0 Reorder the terms: -40 + -4b + b2 = 0 Solving -40 + -4b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -4b + 40 + b2 = 0 + 40 Reorder the terms: -40 + 40 + -4b + b2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -4b + b2 = 0 + 40 -4b + b2 = 0 + 40 Combine like terms: 0 + 40 = 40 -4b + b2 = 40 The b term is -4b. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4b + 4 + b2 = 40 + 4 Reorder the terms: 4 + -4b + b2 = 40 + 4 Combine like terms: 40 + 4 = 44 4 + -4b + b2 = 44 Factor a perfect square on the left side: (b + -2)(b + -2) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (b + -2) equal to 6.633249581 and -6.633249581.Subproblem 1
b + -2 = 6.633249581 Simplifying b + -2 = 6.633249581 Reorder the terms: -2 + b = 6.633249581 Solving -2 + b = 6.633249581 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = 6.633249581 + 2 Combine like terms: -2 + 2 = 0 0 + b = 6.633249581 + 2 b = 6.633249581 + 2 Combine like terms: 6.633249581 + 2 = 8.633249581 b = 8.633249581 Simplifying b = 8.633249581Subproblem 2
b + -2 = -6.633249581 Simplifying b + -2 = -6.633249581 Reorder the terms: -2 + b = -6.633249581 Solving -2 + b = -6.633249581 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = -6.633249581 + 2 Combine like terms: -2 + 2 = 0 0 + b = -6.633249581 + 2 b = -6.633249581 + 2 Combine like terms: -6.633249581 + 2 = -4.633249581 b = -4.633249581 Simplifying b = -4.633249581Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.633249581, -4.633249581}
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