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Simplifying 12b2 + 8b = 6 Reorder the terms: 8b + 12b2 = 6 Solving 8b + 12b2 = 6 Solving for variable 'b'. Reorder the terms: -6 + 8b + 12b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 8b + 12b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4b + 6b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4b + 6b2)' equal to zero and attempt to solve: Simplifying -3 + 4b + 6b2 = 0 Solving -3 + 4b + 6b2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.6666666667b + b2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.6666666667b + 0.5 + b2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.6666666667b + b2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.6666666667b + b2 = 0 + 0.5 0.6666666667b + b2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.6666666667b + b2 = 0.5 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 = 0.5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667b + b2 = 0.5 + 0.1111111112 Combine like terms: 0.5 + 0.1111111112 = 0.6111111112 0.1111111112 + 0.6666666667b + b2 = 0.6111111112 Factor a perfect square on the left side: (b + 0.3333333334)(b + 0.3333333334) = 0.6111111112 Calculate the square root of the right side: 0.78173596 Break this problem into two subproblems by setting (b + 0.3333333334) equal to 0.78173596 and -0.78173596.Subproblem 1
b + 0.3333333334 = 0.78173596 Simplifying b + 0.3333333334 = 0.78173596 Reorder the terms: 0.3333333334 + b = 0.78173596 Solving 0.3333333334 + b = 0.78173596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + b = 0.78173596 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + b = 0.78173596 + -0.3333333334 b = 0.78173596 + -0.3333333334 Combine like terms: 0.78173596 + -0.3333333334 = 0.4484026266 b = 0.4484026266 Simplifying b = 0.4484026266Subproblem 2
b + 0.3333333334 = -0.78173596 Simplifying b + 0.3333333334 = -0.78173596 Reorder the terms: 0.3333333334 + b = -0.78173596 Solving 0.3333333334 + b = -0.78173596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + b = -0.78173596 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + b = -0.78173596 + -0.3333333334 b = -0.78173596 + -0.3333333334 Combine like terms: -0.78173596 + -0.3333333334 = -1.1150692934 b = -1.1150692934 Simplifying b = -1.1150692934Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.4484026266, -1.1150692934}Solution
b = {0.4484026266, -1.1150692934}
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