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Simplifying 4B + B2 = 180 Solving 4B + B2 = 180 Solving for variable 'B'. Reorder the terms: -180 + 4B + B2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 4B + B2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 4B + 180 + B2 = 0 + 180 Reorder the terms: -180 + 180 + 4B + B2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 4B + B2 = 0 + 180 4B + B2 = 0 + 180 Combine like terms: 0 + 180 = 180 4B + B2 = 180 The B term is 4B. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4B + 4 + B2 = 180 + 4 Reorder the terms: 4 + 4B + B2 = 180 + 4 Combine like terms: 180 + 4 = 184 4 + 4B + B2 = 184 Factor a perfect square on the left side: (B + 2)(B + 2) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (B + 2) equal to 13.564659966 and -13.564659966.Subproblem 1
B + 2 = 13.564659966 Simplifying B + 2 = 13.564659966 Reorder the terms: 2 + B = 13.564659966 Solving 2 + B = 13.564659966 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + B = 13.564659966 + -2 Combine like terms: 2 + -2 = 0 0 + B = 13.564659966 + -2 B = 13.564659966 + -2 Combine like terms: 13.564659966 + -2 = 11.564659966 B = 11.564659966 Simplifying B = 11.564659966Subproblem 2
B + 2 = -13.564659966 Simplifying B + 2 = -13.564659966 Reorder the terms: 2 + B = -13.564659966 Solving 2 + B = -13.564659966 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + B = -13.564659966 + -2 Combine like terms: 2 + -2 = 0 0 + B = -13.564659966 + -2 B = -13.564659966 + -2 Combine like terms: -13.564659966 + -2 = -15.564659966 B = -15.564659966 Simplifying B = -15.564659966Solution
The solution to the problem is based on the solutions from the subproblems. B = {11.564659966, -15.564659966}
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