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Simplifying 3b2 + -2b = 3 Reorder the terms: -2b + 3b2 = 3 Solving -2b + 3b2 = 3 Solving for variable 'b'. Reorder the terms: -3 + -2b + 3b2 = 3 + -3 Combine like terms: 3 + -3 = 0 -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 = 1.1111111112 0.1111111112 + -0.6666666667b + b2 = 1.1111111112 Factor a perfect square on the left side: (b + -0.3333333334)(b + -0.3333333334) = 1.1111111112 Calculate the square root of the right side: 1.054092553 Break this problem into two subproblems by setting (b + -0.3333333334) equal to 1.054092553 and -1.054092553.Subproblem 1
b + -0.3333333334 = 1.054092553 Simplifying b + -0.3333333334 = 1.054092553 Reorder the terms: -0.3333333334 + b = 1.054092553 Solving -0.3333333334 + b = 1.054092553 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 = 1.054092553 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + b = 1.054092553 + 0.3333333334 b = 1.054092553 + 0.3333333334 Combine like terms: 1.054092553 + 0.3333333334 = 1.3874258864 b = 1.3874258864 Simplifying b = 1.3874258864Subproblem 2
b + -0.3333333334 = -1.054092553 Simplifying b + -0.3333333334 = -1.054092553 Reorder the terms: -0.3333333334 + b = -1.054092553 Solving -0.3333333334 + b = -1.054092553 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 = -1.054092553 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + b = -1.054092553 + 0.3333333334 b = -1.054092553 + 0.3333333334 Combine like terms: -1.054092553 + 0.3333333334 = -0.7207592196 b = -0.7207592196 Simplifying b = -0.7207592196Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.3874258864, -0.7207592196}
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