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Simplifying 3b2 + 7b + -3 = 0 Reorder the terms: -3 + 7b + 3b2 = 0 Solving -3 + 7b + 3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 2.333333333b + b2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2.333333333b + 1 + b2 = 0 + 1 Reorder the terms: -1 + 1 + 2.333333333b + b2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2.333333333b + b2 = 0 + 1 2.333333333b + b2 = 0 + 1 Combine like terms: 0 + 1 = 1 2.333333333b + b2 = 1 The b term is 2.333333333b. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333b + 1.361111112 + b2 = 1 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333b + b2 = 1 + 1.361111112 Combine like terms: 1 + 1.361111112 = 2.361111112 1.361111112 + 2.333333333b + b2 = 2.361111112 Factor a perfect square on the left side: (b + 1.166666667)(b + 1.166666667) = 2.361111112 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (b + 1.166666667) equal to 1.536590743 and -1.536590743.Subproblem 1
b + 1.166666667 = 1.536590743 Simplifying b + 1.166666667 = 1.536590743 Reorder the terms: 1.166666667 + b = 1.536590743 Solving 1.166666667 + b = 1.536590743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + b = 1.536590743 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + b = 1.536590743 + -1.166666667 b = 1.536590743 + -1.166666667 Combine like terms: 1.536590743 + -1.166666667 = 0.369924076 b = 0.369924076 Simplifying b = 0.369924076Subproblem 2
b + 1.166666667 = -1.536590743 Simplifying b + 1.166666667 = -1.536590743 Reorder the terms: 1.166666667 + b = -1.536590743 Solving 1.166666667 + b = -1.536590743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + b = -1.536590743 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + b = -1.536590743 + -1.166666667 b = -1.536590743 + -1.166666667 Combine like terms: -1.536590743 + -1.166666667 = -2.70325741 b = -2.70325741 Simplifying b = -2.70325741Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.369924076, -2.70325741}
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