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Simplifying 5b2 = 36 + -10b Solving 5b2 = 36 + -10b Solving for variable 'b'. Reorder the terms: -36 + 10b + 5b2 = 36 + -10b + -36 + 10b Reorder the terms: -36 + 10b + 5b2 = 36 + -36 + -10b + 10b Combine like terms: 36 + -36 = 0 -36 + 10b + 5b2 = 0 + -10b + 10b -36 + 10b + 5b2 = -10b + 10b Combine like terms: -10b + 10b = 0 -36 + 10b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 2b + b2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 2b + 7.2 + b2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 2b + b2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 2b + b2 = 0 + 7.2 2b + b2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 2b + b2 = 7.2 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = 7.2 + 1 Reorder the terms: 1 + 2b + b2 = 7.2 + 1 Combine like terms: 7.2 + 1 = 8.2 1 + 2b + b2 = 8.2 Factor a perfect square on the left side: (b + 1)(b + 1) = 8.2 Calculate the square root of the right side: 2.863564213 Break this problem into two subproblems by setting (b + 1) equal to 2.863564213 and -2.863564213.Subproblem 1
b + 1 = 2.863564213 Simplifying b + 1 = 2.863564213 Reorder the terms: 1 + b = 2.863564213 Solving 1 + b = 2.863564213 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 2.863564213 + -1 Combine like terms: 1 + -1 = 0 0 + b = 2.863564213 + -1 b = 2.863564213 + -1 Combine like terms: 2.863564213 + -1 = 1.863564213 b = 1.863564213 Simplifying b = 1.863564213Subproblem 2
b + 1 = -2.863564213 Simplifying b + 1 = -2.863564213 Reorder the terms: 1 + b = -2.863564213 Solving 1 + b = -2.863564213 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -2.863564213 + -1 Combine like terms: 1 + -1 = 0 0 + b = -2.863564213 + -1 b = -2.863564213 + -1 Combine like terms: -2.863564213 + -1 = -3.863564213 b = -3.863564213 Simplifying b = -3.863564213Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.863564213, -3.863564213}
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