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Simplifying B(B + -150) = 225000 Reorder the terms: B(-150 + B) = 225000 (-150 * B + B * B) = 225000 (-150B + B2) = 225000 Solving -150B + B2 = 225000 Solving for variable 'B'. Reorder the terms: -225000 + -150B + B2 = 225000 + -225000 Combine like terms: 225000 + -225000 = 0 -225000 + -150B + B2 = 0 Begin completing the square. Move the constant term to the right: Add '225000' to each side of the equation. -225000 + -150B + 225000 + B2 = 0 + 225000 Reorder the terms: -225000 + 225000 + -150B + B2 = 0 + 225000 Combine like terms: -225000 + 225000 = 0 0 + -150B + B2 = 0 + 225000 -150B + B2 = 0 + 225000 Combine like terms: 0 + 225000 = 225000 -150B + B2 = 225000 The B term is -150B. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150B + 5625 + B2 = 225000 + 5625 Reorder the terms: 5625 + -150B + B2 = 225000 + 5625 Combine like terms: 225000 + 5625 = 230625 5625 + -150B + B2 = 230625 Factor a perfect square on the left side: (B + -75)(B + -75) = 230625 Calculate the square root of the right side: 480.234317807 Break this problem into two subproblems by setting (B + -75) equal to 480.234317807 and -480.234317807.Subproblem 1
B + -75 = 480.234317807 Simplifying B + -75 = 480.234317807 Reorder the terms: -75 + B = 480.234317807 Solving -75 + B = 480.234317807 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + B = 480.234317807 + 75 Combine like terms: -75 + 75 = 0 0 + B = 480.234317807 + 75 B = 480.234317807 + 75 Combine like terms: 480.234317807 + 75 = 555.234317807 B = 555.234317807 Simplifying B = 555.234317807Subproblem 2
B + -75 = -480.234317807 Simplifying B + -75 = -480.234317807 Reorder the terms: -75 + B = -480.234317807 Solving -75 + B = -480.234317807 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + B = -480.234317807 + 75 Combine like terms: -75 + 75 = 0 0 + B = -480.234317807 + 75 B = -480.234317807 + 75 Combine like terms: -480.234317807 + 75 = -405.234317807 B = -405.234317807 Simplifying B = -405.234317807Solution
The solution to the problem is based on the solutions from the subproblems. B = {555.234317807, -405.234317807}
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