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Simplifying (4b2 + 6b) + (2b + -15) = 0 Reorder the terms: (6b + 4b2) + (2b + -15) = 0 Remove parenthesis around (6b + 4b2) 6b + 4b2 + (2b + -15) = 0 Reorder the terms: 6b + 4b2 + (-15 + 2b) = 0 Remove parenthesis around (-15 + 2b) 6b + 4b2 + -15 + 2b = 0 Reorder the terms: -15 + 6b + 2b + 4b2 = 0 Combine like terms: 6b + 2b = 8b -15 + 8b + 4b2 = 0 Solving -15 + 8b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 2b + b2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2b + 3.75 + b2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2b + b2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2b + b2 = 0 + 3.75 2b + b2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2b + b2 = 3.75 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = 3.75 + 1 Reorder the terms: 1 + 2b + b2 = 3.75 + 1 Combine like terms: 3.75 + 1 = 4.75 1 + 2b + b2 = 4.75 Factor a perfect square on the left side: (b + 1)(b + 1) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (b + 1) equal to 2.179449472 and -2.179449472.Subproblem 1
b + 1 = 2.179449472 Simplifying b + 1 = 2.179449472 Reorder the terms: 1 + b = 2.179449472 Solving 1 + b = 2.179449472 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 2.179449472 + -1 Combine like terms: 1 + -1 = 0 0 + b = 2.179449472 + -1 b = 2.179449472 + -1 Combine like terms: 2.179449472 + -1 = 1.179449472 b = 1.179449472 Simplifying b = 1.179449472Subproblem 2
b + 1 = -2.179449472 Simplifying b + 1 = -2.179449472 Reorder the terms: 1 + b = -2.179449472 Solving 1 + b = -2.179449472 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -2.179449472 + -1 Combine like terms: 1 + -1 = 0 0 + b = -2.179449472 + -1 b = -2.179449472 + -1 Combine like terms: -2.179449472 + -1 = -3.179449472 b = -3.179449472 Simplifying b = -3.179449472Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.179449472, -3.179449472}
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