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Simplifying B2 + 7B + -33 = 0 Reorder the terms: -33 + 7B + B2 = 0 Solving -33 + 7B + B2 = 0 Solving for variable 'B'. Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 7B + 33 + B2 = 0 + 33 Reorder the terms: -33 + 33 + 7B + B2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 7B + B2 = 0 + 33 7B + B2 = 0 + 33 Combine like terms: 0 + 33 = 33 7B + B2 = 33 The B term is 7B. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7B + 12.25 + B2 = 33 + 12.25 Reorder the terms: 12.25 + 7B + B2 = 33 + 12.25 Combine like terms: 33 + 12.25 = 45.25 12.25 + 7B + B2 = 45.25 Factor a perfect square on the left side: (B + 3.5)(B + 3.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (B + 3.5) equal to 6.726812024 and -6.726812024.Subproblem 1
B + 3.5 = 6.726812024 Simplifying B + 3.5 = 6.726812024 Reorder the terms: 3.5 + B = 6.726812024 Solving 3.5 + B = 6.726812024 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + B = 6.726812024 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + B = 6.726812024 + -3.5 B = 6.726812024 + -3.5 Combine like terms: 6.726812024 + -3.5 = 3.226812024 B = 3.226812024 Simplifying B = 3.226812024Subproblem 2
B + 3.5 = -6.726812024 Simplifying B + 3.5 = -6.726812024 Reorder the terms: 3.5 + B = -6.726812024 Solving 3.5 + B = -6.726812024 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + B = -6.726812024 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + B = -6.726812024 + -3.5 B = -6.726812024 + -3.5 Combine like terms: -6.726812024 + -3.5 = -10.226812024 B = -10.226812024 Simplifying B = -10.226812024Solution
The solution to the problem is based on the solutions from the subproblems. B = {3.226812024, -10.226812024}
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