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Simplifying 40 = b(b + 4) Reorder the terms: 40 = b(4 + b) 40 = (4 * b + b * b) 40 = (4b + b2) Solving 40 = 4b + b2 Solving for variable 'b'. Reorder the terms: 40 + -4b + -1b2 = 4b + -4b + b2 + -1b2 Combine like terms: 4b + -4b = 0 40 + -4b + -1b2 = 0 + b2 + -1b2 40 + -4b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 40 + -4b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 4b + b2 = 0 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 = 4.633249581 b = 4.633249581 Simplifying b = 4.633249581Subproblem 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 = -8.633249581 b = -8.633249581 Simplifying b = -8.633249581Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.633249581, -8.633249581}
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