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Simplifying -1b(b + -3) + -1(4b + -7) = 3b + 4 Reorder the terms: -1b(-3 + b) + -1(4b + -7) = 3b + 4 (-3 * -1b + b * -1b) + -1(4b + -7) = 3b + 4 (3b + -1b2) + -1(4b + -7) = 3b + 4 Reorder the terms: 3b + -1b2 + -1(-7 + 4b) = 3b + 4 3b + -1b2 + (-7 * -1 + 4b * -1) = 3b + 4 3b + -1b2 + (7 + -4b) = 3b + 4 Reorder the terms: 7 + 3b + -4b + -1b2 = 3b + 4 Combine like terms: 3b + -4b = -1b 7 + -1b + -1b2 = 3b + 4 Reorder the terms: 7 + -1b + -1b2 = 4 + 3b Solving 7 + -1b + -1b2 = 4 + 3b Solving for variable 'b'. Reorder the terms: 7 + -4 + -1b + -3b + -1b2 = 4 + 3b + -4 + -3b Combine like terms: 7 + -4 = 3 3 + -1b + -3b + -1b2 = 4 + 3b + -4 + -3b Combine like terms: -1b + -3b = -4b 3 + -4b + -1b2 = 4 + 3b + -4 + -3b Reorder the terms: 3 + -4b + -1b2 = 4 + -4 + 3b + -3b Combine like terms: 4 + -4 = 0 3 + -4b + -1b2 = 0 + 3b + -3b 3 + -4b + -1b2 = 3b + -3b Combine like terms: 3b + -3b = 0 3 + -4b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 4b + b2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + 4b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4b + b2 = 0 + 3 4b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 4b + b2 = 3 The b term is 4b. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4b + 4 + b2 = 3 + 4 Reorder the terms: 4 + 4b + b2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4b + b2 = 7 Factor a perfect square on the left side: (b + 2)(b + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (b + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
b + 2 = 2.645751311 Simplifying b + 2 = 2.645751311 Reorder the terms: 2 + b = 2.645751311 Solving 2 + b = 2.645751311 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + b = 2.645751311 + -2 b = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 b = 0.645751311 Simplifying b = 0.645751311Subproblem 2
b + 2 = -2.645751311 Simplifying b + 2 = -2.645751311 Reorder the terms: 2 + b = -2.645751311 Solving 2 + b = -2.645751311 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + b = -2.645751311 + -2 b = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 b = -4.645751311 Simplifying b = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.645751311, -4.645751311}
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