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Simplifying b2 + -30b + 40 = 0 Reorder the terms: 40 + -30b + b2 = 0 Solving 40 + -30b + 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 + -30b + -40 + b2 = 0 + -40 Reorder the terms: 40 + -40 + -30b + b2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -30b + b2 = 0 + -40 -30b + b2 = 0 + -40 Combine like terms: 0 + -40 = -40 -30b + b2 = -40 The b term is -30b. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30b + 225 + b2 = -40 + 225 Reorder the terms: 225 + -30b + b2 = -40 + 225 Combine like terms: -40 + 225 = 185 225 + -30b + b2 = 185 Factor a perfect square on the left side: (b + -15)(b + -15) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (b + -15) equal to 13.601470509 and -13.601470509.Subproblem 1
b + -15 = 13.601470509 Simplifying b + -15 = 13.601470509 Reorder the terms: -15 + b = 13.601470509 Solving -15 + b = 13.601470509 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + b = 13.601470509 + 15 Combine like terms: -15 + 15 = 0 0 + b = 13.601470509 + 15 b = 13.601470509 + 15 Combine like terms: 13.601470509 + 15 = 28.601470509 b = 28.601470509 Simplifying b = 28.601470509Subproblem 2
b + -15 = -13.601470509 Simplifying b + -15 = -13.601470509 Reorder the terms: -15 + b = -13.601470509 Solving -15 + b = -13.601470509 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + b = -13.601470509 + 15 Combine like terms: -15 + 15 = 0 0 + b = -13.601470509 + 15 b = -13.601470509 + 15 Combine like terms: -13.601470509 + 15 = 1.398529491 b = 1.398529491 Simplifying b = 1.398529491Solution
The solution to the problem is based on the solutions from the subproblems. b = {28.601470509, 1.398529491}
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