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Simplifying 11B2 + 2B + -186 = 0 Reorder the terms: -186 + 2B + 11B2 = 0 Solving -186 + 2B + 11B2 = 0 Solving for variable 'B'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -16.90909091 + 0.1818181818B + B2 = 0 Move the constant term to the right: Add '16.90909091' to each side of the equation. -16.90909091 + 0.1818181818B + 16.90909091 + B2 = 0 + 16.90909091 Reorder the terms: -16.90909091 + 16.90909091 + 0.1818181818B + B2 = 0 + 16.90909091 Combine like terms: -16.90909091 + 16.90909091 = 0.00000000 0.00000000 + 0.1818181818B + B2 = 0 + 16.90909091 0.1818181818B + B2 = 0 + 16.90909091 Combine like terms: 0 + 16.90909091 = 16.90909091 0.1818181818B + B2 = 16.90909091 The B term is 0.1818181818B. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818B + 0.008264462808 + B2 = 16.90909091 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818B + B2 = 16.90909091 + 0.008264462808 Combine like terms: 16.90909091 + 0.008264462808 = 16.917355372808 0.008264462808 + 0.1818181818B + B2 = 16.917355372808 Factor a perfect square on the left side: (B + 0.0909090909)(B + 0.0909090909) = 16.917355372808 Calculate the square root of the right side: 4.113071282 Break this problem into two subproblems by setting (B + 0.0909090909) equal to 4.113071282 and -4.113071282.Subproblem 1
B + 0.0909090909 = 4.113071282 Simplifying B + 0.0909090909 = 4.113071282 Reorder the terms: 0.0909090909 + B = 4.113071282 Solving 0.0909090909 + B = 4.113071282 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + B = 4.113071282 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + B = 4.113071282 + -0.0909090909 B = 4.113071282 + -0.0909090909 Combine like terms: 4.113071282 + -0.0909090909 = 4.0221621911 B = 4.0221621911 Simplifying B = 4.0221621911Subproblem 2
B + 0.0909090909 = -4.113071282 Simplifying B + 0.0909090909 = -4.113071282 Reorder the terms: 0.0909090909 + B = -4.113071282 Solving 0.0909090909 + B = -4.113071282 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + B = -4.113071282 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + B = -4.113071282 + -0.0909090909 B = -4.113071282 + -0.0909090909 Combine like terms: -4.113071282 + -0.0909090909 = -4.2039803729 B = -4.2039803729 Simplifying B = -4.2039803729Solution
The solution to the problem is based on the solutions from the subproblems. B = {4.0221621911, -4.2039803729}
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