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Simplifying 2b2 + 15b + 26 = 0 Reorder the terms: 26 + 15b + 2b2 = 0 Solving 26 + 15b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13 + 7.5b + b2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + 7.5b + -13 + b2 = 0 + -13 Reorder the terms: 13 + -13 + 7.5b + b2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 7.5b + b2 = 0 + -13 7.5b + b2 = 0 + -13 Combine like terms: 0 + -13 = -13 7.5b + b2 = -13 The b term is 7.5b. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5b + 14.0625 + b2 = -13 + 14.0625 Reorder the terms: 14.0625 + 7.5b + b2 = -13 + 14.0625 Combine like terms: -13 + 14.0625 = 1.0625 14.0625 + 7.5b + b2 = 1.0625 Factor a perfect square on the left side: (b + 3.75)(b + 3.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (b + 3.75) equal to 1.030776406 and -1.030776406.Subproblem 1
b + 3.75 = 1.030776406 Simplifying b + 3.75 = 1.030776406 Reorder the terms: 3.75 + b = 1.030776406 Solving 3.75 + b = 1.030776406 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + b = 1.030776406 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + b = 1.030776406 + -3.75 b = 1.030776406 + -3.75 Combine like terms: 1.030776406 + -3.75 = -2.719223594 b = -2.719223594 Simplifying b = -2.719223594Subproblem 2
b + 3.75 = -1.030776406 Simplifying b + 3.75 = -1.030776406 Reorder the terms: 3.75 + b = -1.030776406 Solving 3.75 + b = -1.030776406 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + b = -1.030776406 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + b = -1.030776406 + -3.75 b = -1.030776406 + -3.75 Combine like terms: -1.030776406 + -3.75 = -4.780776406 b = -4.780776406 Simplifying b = -4.780776406Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.719223594, -4.780776406}
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