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Simplifying 9b2 + -80b + -20 = 0 Reorder the terms: -20 + -80b + 9b2 = 0 Solving -20 + -80b + 9b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -8.888888889b + b2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -8.888888889b + 2.222222222 + b2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -8.888888889b + b2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -8.888888889b + b2 = 0 + 2.222222222 -8.888888889b + b2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -8.888888889b + b2 = 2.222222222 The b term is -8.888888889b. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889b + 19.75308642 + b2 = 2.222222222 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889b + b2 = 2.222222222 + 19.75308642 Combine like terms: 2.222222222 + 19.75308642 = 21.975308642 19.75308642 + -8.888888889b + b2 = 21.975308642 Factor a perfect square on the left side: (b + -4.444444445)(b + -4.444444445) = 21.975308642 Calculate the square root of the right side: 4.687782913 Break this problem into two subproblems by setting (b + -4.444444445) equal to 4.687782913 and -4.687782913.Subproblem 1
b + -4.444444445 = 4.687782913 Simplifying b + -4.444444445 = 4.687782913 Reorder the terms: -4.444444445 + b = 4.687782913 Solving -4.444444445 + b = 4.687782913 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + b = 4.687782913 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + b = 4.687782913 + 4.444444445 b = 4.687782913 + 4.444444445 Combine like terms: 4.687782913 + 4.444444445 = 9.132227358 b = 9.132227358 Simplifying b = 9.132227358Subproblem 2
b + -4.444444445 = -4.687782913 Simplifying b + -4.444444445 = -4.687782913 Reorder the terms: -4.444444445 + b = -4.687782913 Solving -4.444444445 + b = -4.687782913 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + b = -4.687782913 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + b = -4.687782913 + 4.444444445 b = -4.687782913 + 4.444444445 Combine like terms: -4.687782913 + 4.444444445 = -0.243338468 b = -0.243338468 Simplifying b = -0.243338468Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.132227358, -0.243338468}
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