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Simplifying 2b2 + 9b + -13 = 4b Reorder the terms: -13 + 9b + 2b2 = 4b Solving -13 + 9b + 2b2 = 4b Solving for variable 'b'. Reorder the terms: -13 + 9b + -4b + 2b2 = 4b + -4b Combine like terms: 9b + -4b = 5b -13 + 5b + 2b2 = 4b + -4b Combine like terms: 4b + -4b = 0 -13 + 5b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 2.5b + b2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 2.5b + 6.5 + b2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 2.5b + b2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 2.5b + b2 = 0 + 6.5 2.5b + b2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 2.5b + b2 = 6.5 The b term is 2.5b. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5b + 1.5625 + b2 = 6.5 + 1.5625 Reorder the terms: 1.5625 + 2.5b + b2 = 6.5 + 1.5625 Combine like terms: 6.5 + 1.5625 = 8.0625 1.5625 + 2.5b + b2 = 8.0625 Factor a perfect square on the left side: (b + 1.25)(b + 1.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (b + 1.25) equal to 2.839454173 and -2.839454173.Subproblem 1
b + 1.25 = 2.839454173 Simplifying b + 1.25 = 2.839454173 Reorder the terms: 1.25 + b = 2.839454173 Solving 1.25 + b = 2.839454173 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = 2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = 2.839454173 + -1.25 b = 2.839454173 + -1.25 Combine like terms: 2.839454173 + -1.25 = 1.589454173 b = 1.589454173 Simplifying b = 1.589454173Subproblem 2
b + 1.25 = -2.839454173 Simplifying b + 1.25 = -2.839454173 Reorder the terms: 1.25 + b = -2.839454173 Solving 1.25 + b = -2.839454173 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = -2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = -2.839454173 + -1.25 b = -2.839454173 + -1.25 Combine like terms: -2.839454173 + -1.25 = -4.089454173 b = -4.089454173 Simplifying b = -4.089454173Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.589454173, -4.089454173}
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