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Simplifying 9b2 + -17b + -34 = 0 Reorder the terms: -34 + -17b + 9b2 = 0 Solving -34 + -17b + 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'. -3.777777778 + -1.888888889b + b2 = 0 Move the constant term to the right: Add '3.777777778' to each side of the equation. -3.777777778 + -1.888888889b + 3.777777778 + b2 = 0 + 3.777777778 Reorder the terms: -3.777777778 + 3.777777778 + -1.888888889b + b2 = 0 + 3.777777778 Combine like terms: -3.777777778 + 3.777777778 = 0.000000000 0.000000000 + -1.888888889b + b2 = 0 + 3.777777778 -1.888888889b + b2 = 0 + 3.777777778 Combine like terms: 0 + 3.777777778 = 3.777777778 -1.888888889b + b2 = 3.777777778 The b term is -1.888888889b. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889b + 0.8919753087 + b2 = 3.777777778 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889b + b2 = 3.777777778 + 0.8919753087 Combine like terms: 3.777777778 + 0.8919753087 = 4.6697530867 0.8919753087 + -1.888888889b + b2 = 4.6697530867 Factor a perfect square on the left side: (b + -0.9444444445)(b + -0.9444444445) = 4.6697530867 Calculate the square root of the right side: 2.160961149 Break this problem into two subproblems by setting (b + -0.9444444445) equal to 2.160961149 and -2.160961149.Subproblem 1
b + -0.9444444445 = 2.160961149 Simplifying b + -0.9444444445 = 2.160961149 Reorder the terms: -0.9444444445 + b = 2.160961149 Solving -0.9444444445 + b = 2.160961149 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + b = 2.160961149 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + b = 2.160961149 + 0.9444444445 b = 2.160961149 + 0.9444444445 Combine like terms: 2.160961149 + 0.9444444445 = 3.1054055935 b = 3.1054055935 Simplifying b = 3.1054055935Subproblem 2
b + -0.9444444445 = -2.160961149 Simplifying b + -0.9444444445 = -2.160961149 Reorder the terms: -0.9444444445 + b = -2.160961149 Solving -0.9444444445 + b = -2.160961149 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + b = -2.160961149 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + b = -2.160961149 + 0.9444444445 b = -2.160961149 + 0.9444444445 Combine like terms: -2.160961149 + 0.9444444445 = -1.2165167045 b = -1.2165167045 Simplifying b = -1.2165167045Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.1054055935, -1.2165167045}
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