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Simplifying 3b2 + -15b + 11 = -6 Reorder the terms: 11 + -15b + 3b2 = -6 Solving 11 + -15b + 3b2 = -6 Solving for variable 'b'. Reorder the terms: 11 + 6 + -15b + 3b2 = -6 + 6 Combine like terms: 11 + 6 = 17 17 + -15b + 3b2 = -6 + 6 Combine like terms: -6 + 6 = 0 17 + -15b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.666666667 + -5b + b2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + -5b + -5.666666667 + b2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + -5b + b2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + -5b + b2 = 0 + -5.666666667 -5b + b2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 -5b + b2 = -5.666666667 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = -5.666666667 + 6.25 Reorder the terms: 6.25 + -5b + b2 = -5.666666667 + 6.25 Combine like terms: -5.666666667 + 6.25 = 0.583333333 6.25 + -5b + b2 = 0.583333333 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 0.583333333 Calculate the square root of the right side: 0.763762616 Break this problem into two subproblems by setting (b + -2.5) equal to 0.763762616 and -0.763762616.Subproblem 1
b + -2.5 = 0.763762616 Simplifying b + -2.5 = 0.763762616 Reorder the terms: -2.5 + b = 0.763762616 Solving -2.5 + b = 0.763762616 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 0.763762616 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 0.763762616 + 2.5 b = 0.763762616 + 2.5 Combine like terms: 0.763762616 + 2.5 = 3.263762616 b = 3.263762616 Simplifying b = 3.263762616Subproblem 2
b + -2.5 = -0.763762616 Simplifying b + -2.5 = -0.763762616 Reorder the terms: -2.5 + b = -0.763762616 Solving -2.5 + b = -0.763762616 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -0.763762616 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -0.763762616 + 2.5 b = -0.763762616 + 2.5 Combine like terms: -0.763762616 + 2.5 = 1.736237384 b = 1.736237384 Simplifying b = 1.736237384Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.263762616, 1.736237384}
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