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Simplifying -9(B2 + 2B) + -3 + B(2B + 5) + 7 = 0 Reorder the terms: -9(2B + B2) + -3 + B(2B + 5) + 7 = 0 (2B * -9 + B2 * -9) + -3 + B(2B + 5) + 7 = 0 (-18B + -9B2) + -3 + B(2B + 5) + 7 = 0 Reorder the terms: -18B + -9B2 + -3 + B(5 + 2B) + 7 = 0 -18B + -9B2 + -3 + (5 * B + 2B * B) + 7 = 0 -18B + -9B2 + -3 + (5B + 2B2) + 7 = 0 Reorder the terms: -3 + 7 + -18B + 5B + -9B2 + 2B2 = 0 Combine like terms: -3 + 7 = 4 4 + -18B + 5B + -9B2 + 2B2 = 0 Combine like terms: -18B + 5B = -13B 4 + -13B + -9B2 + 2B2 = 0 Combine like terms: -9B2 + 2B2 = -7B2 4 + -13B + -7B2 = 0 Solving 4 + -13B + -7B2 = 0 Solving for variable 'B'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + 1.857142857B + B2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 1.857142857B + 0.5714285714 + B2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 1.857142857B + B2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 1.857142857B + B2 = 0 + 0.5714285714 1.857142857B + B2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 1.857142857B + B2 = 0.5714285714 The B term is 1.857142857B. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857B + 0.8622448978 + B2 = 0.5714285714 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857B + B2 = 0.5714285714 + 0.8622448978 Combine like terms: 0.5714285714 + 0.8622448978 = 1.4336734692 0.8622448978 + 1.857142857B + B2 = 1.4336734692 Factor a perfect square on the left side: (B + 0.9285714285)(B + 0.9285714285) = 1.4336734692 Calculate the square root of the right side: 1.197361044 Break this problem into two subproblems by setting (B + 0.9285714285) equal to 1.197361044 and -1.197361044.Subproblem 1
B + 0.9285714285 = 1.197361044 Simplifying B + 0.9285714285 = 1.197361044 Reorder the terms: 0.9285714285 + B = 1.197361044 Solving 0.9285714285 + B = 1.197361044 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + B = 1.197361044 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + B = 1.197361044 + -0.9285714285 B = 1.197361044 + -0.9285714285 Combine like terms: 1.197361044 + -0.9285714285 = 0.2687896155 B = 0.2687896155 Simplifying B = 0.2687896155Subproblem 2
B + 0.9285714285 = -1.197361044 Simplifying B + 0.9285714285 = -1.197361044 Reorder the terms: 0.9285714285 + B = -1.197361044 Solving 0.9285714285 + B = -1.197361044 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + B = -1.197361044 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + B = -1.197361044 + -0.9285714285 B = -1.197361044 + -0.9285714285 Combine like terms: -1.197361044 + -0.9285714285 = -2.1259324725 B = -2.1259324725 Simplifying B = -2.1259324725Solution
The solution to the problem is based on the solutions from the subproblems. B = {0.2687896155, -2.1259324725}
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