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Simplifying -5B2 + 51B = 15 Reorder the terms: 51B + -5B2 = 15 Solving 51B + -5B2 = 15 Solving for variable 'B'. Reorder the terms: -15 + 51B + -5B2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 51B + -5B2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3 + -10.2B + B2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10.2B + -3 + B2 = 0 + -3 Reorder the terms: 3 + -3 + -10.2B + B2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10.2B + B2 = 0 + -3 -10.2B + B2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10.2B + B2 = -3 The B term is -10.2B. Take half its coefficient (-5.1). Square it (26.01) and add it to both sides. Add '26.01' to each side of the equation. -10.2B + 26.01 + B2 = -3 + 26.01 Reorder the terms: 26.01 + -10.2B + B2 = -3 + 26.01 Combine like terms: -3 + 26.01 = 23.01 26.01 + -10.2B + B2 = 23.01 Factor a perfect square on the left side: (B + -5.1)(B + -5.1) = 23.01 Calculate the square root of the right side: 4.796873982 Break this problem into two subproblems by setting (B + -5.1) equal to 4.796873982 and -4.796873982.Subproblem 1
B + -5.1 = 4.796873982 Simplifying B + -5.1 = 4.796873982 Reorder the terms: -5.1 + B = 4.796873982 Solving -5.1 + B = 4.796873982 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + B = 4.796873982 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + B = 4.796873982 + 5.1 B = 4.796873982 + 5.1 Combine like terms: 4.796873982 + 5.1 = 9.896873982 B = 9.896873982 Simplifying B = 9.896873982Subproblem 2
B + -5.1 = -4.796873982 Simplifying B + -5.1 = -4.796873982 Reorder the terms: -5.1 + B = -4.796873982 Solving -5.1 + B = -4.796873982 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + B = -4.796873982 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + B = -4.796873982 + 5.1 B = -4.796873982 + 5.1 Combine like terms: -4.796873982 + 5.1 = 0.303126018 B = 0.303126018 Simplifying B = 0.303126018Solution
The solution to the problem is based on the solutions from the subproblems. B = {9.896873982, 0.303126018}
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