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Simplifying 6b(1 + 3b) + -2(-4b + -3) = 0 (1 * 6b + 3b * 6b) + -2(-4b + -3) = 0 (6b + 18b2) + -2(-4b + -3) = 0 Reorder the terms: 6b + 18b2 + -2(-3 + -4b) = 0 6b + 18b2 + (-3 * -2 + -4b * -2) = 0 6b + 18b2 + (6 + 8b) = 0 Reorder the terms: 6 + 6b + 8b + 18b2 = 0 Combine like terms: 6b + 8b = 14b 6 + 14b + 18b2 = 0 Solving 6 + 14b + 18b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 7b + 9b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 7b + 9b2)' equal to zero and attempt to solve: Simplifying 3 + 7b + 9b2 = 0 Solving 3 + 7b + 9b2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + 0.7777777778b + b2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.7777777778b + -0.3333333333 + b2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.7777777778b + b2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.7777777778b + b2 = 0 + -0.3333333333 0.7777777778b + b2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.7777777778b + b2 = -0.3333333333 The b term is 0.7777777778b. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778b + 0.1512345679 + b2 = -0.3333333333 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778b + b2 = -0.3333333333 + 0.1512345679 Combine like terms: -0.3333333333 + 0.1512345679 = -0.1820987654 0.1512345679 + 0.7777777778b + b2 = -0.1820987654 Factor a perfect square on the left side: (b + 0.3888888889)(b + 0.3888888889) = -0.1820987654 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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