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Simplifying (4b2 + -8b + 11) + -1(-2b2 + -4b + 5) = 0 Reorder the terms: (11 + -8b + 4b2) + -1(-2b2 + -4b + 5) = 0 Remove parenthesis around (11 + -8b + 4b2) 11 + -8b + 4b2 + -1(-2b2 + -4b + 5) = 0 Reorder the terms: 11 + -8b + 4b2 + -1(5 + -4b + -2b2) = 0 11 + -8b + 4b2 + (5 * -1 + -4b * -1 + -2b2 * -1) = 0 11 + -8b + 4b2 + (-5 + 4b + 2b2) = 0 Reorder the terms: 11 + -5 + -8b + 4b + 4b2 + 2b2 = 0 Combine like terms: 11 + -5 = 6 6 + -8b + 4b + 4b2 + 2b2 = 0 Combine like terms: -8b + 4b = -4b 6 + -4b + 4b2 + 2b2 = 0 Combine like terms: 4b2 + 2b2 = 6b2 6 + -4b + 6b2 = 0 Solving 6 + -4b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -2b + 3b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2b + 3b2)' equal to zero and attempt to solve: Simplifying 3 + -2b + 3b2 = 0 Solving 3 + -2b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -0.6666666667b + b2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.6666666667b + -1 + b2 = 0 + -1 Reorder the terms: 1 + -1 + -0.6666666667b + b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.6666666667b + b2 = 0 + -1 -0.6666666667b + b2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.6666666667b + b2 = -1 The b term is -0.6666666667b. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667b + 0.1111111112 + b2 = -1 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667b + b2 = -1 + 0.1111111112 Combine like terms: -1 + 0.1111111112 = -0.8888888888 0.1111111112 + -0.6666666667b + b2 = -0.8888888888 Factor a perfect square on the left side: (b + -0.3333333334)(b + -0.3333333334) = -0.8888888888 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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