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Simplifying 3b2 + -22b = 6 Reorder the terms: -22b + 3b2 = 6 Solving -22b + 3b2 = 6 Solving for variable 'b'. Reorder the terms: -6 + -22b + 3b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -22b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -7.333333333b + b2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -7.333333333b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -7.333333333b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7.333333333b + b2 = 0 + 2 -7.333333333b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7.333333333b + b2 = 2 The b term is -7.333333333b. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333b + 13.44444445 + b2 = 2 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333b + b2 = 2 + 13.44444445 Combine like terms: 2 + 13.44444445 = 15.44444445 13.44444445 + -7.333333333b + b2 = 15.44444445 Factor a perfect square on the left side: (b + -3.666666667)(b + -3.666666667) = 15.44444445 Calculate the square root of the right side: 3.929942042 Break this problem into two subproblems by setting (b + -3.666666667) equal to 3.929942042 and -3.929942042.Subproblem 1
b + -3.666666667 = 3.929942042 Simplifying b + -3.666666667 = 3.929942042 Reorder the terms: -3.666666667 + b = 3.929942042 Solving -3.666666667 + b = 3.929942042 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + b = 3.929942042 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + b = 3.929942042 + 3.666666667 b = 3.929942042 + 3.666666667 Combine like terms: 3.929942042 + 3.666666667 = 7.596608709 b = 7.596608709 Simplifying b = 7.596608709Subproblem 2
b + -3.666666667 = -3.929942042 Simplifying b + -3.666666667 = -3.929942042 Reorder the terms: -3.666666667 + b = -3.929942042 Solving -3.666666667 + b = -3.929942042 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + b = -3.929942042 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + b = -3.929942042 + 3.666666667 b = -3.929942042 + 3.666666667 Combine like terms: -3.929942042 + 3.666666667 = -0.263275375 b = -0.263275375 Simplifying b = -0.263275375Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.596608709, -0.263275375}
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