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Simplifying 30 + b2 + -37b = 0 Reorder the terms: 30 + -37b + b2 = 0 Solving 30 + -37b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -37b + -30 + b2 = 0 + -30 Reorder the terms: 30 + -30 + -37b + b2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -37b + b2 = 0 + -30 -37b + b2 = 0 + -30 Combine like terms: 0 + -30 = -30 -37b + b2 = -30 The b term is -37b. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37b + 342.25 + b2 = -30 + 342.25 Reorder the terms: 342.25 + -37b + b2 = -30 + 342.25 Combine like terms: -30 + 342.25 = 312.25 342.25 + -37b + b2 = 312.25 Factor a perfect square on the left side: (b + -18.5)(b + -18.5) = 312.25 Calculate the square root of the right side: 17.670597047 Break this problem into two subproblems by setting (b + -18.5) equal to 17.670597047 and -17.670597047.Subproblem 1
b + -18.5 = 17.670597047 Simplifying b + -18.5 = 17.670597047 Reorder the terms: -18.5 + b = 17.670597047 Solving -18.5 + b = 17.670597047 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + b = 17.670597047 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + b = 17.670597047 + 18.5 b = 17.670597047 + 18.5 Combine like terms: 17.670597047 + 18.5 = 36.170597047 b = 36.170597047 Simplifying b = 36.170597047Subproblem 2
b + -18.5 = -17.670597047 Simplifying b + -18.5 = -17.670597047 Reorder the terms: -18.5 + b = -17.670597047 Solving -18.5 + b = -17.670597047 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + b = -17.670597047 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + b = -17.670597047 + 18.5 b = -17.670597047 + 18.5 Combine like terms: -17.670597047 + 18.5 = 0.829402953 b = 0.829402953 Simplifying b = 0.829402953Solution
The solution to the problem is based on the solutions from the subproblems. b = {36.170597047, 0.829402953}
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