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Simplifying B2 + 7 = B + 17 Reorder the terms: 7 + B2 = B + 17 Reorder the terms: 7 + B2 = 17 + B Solving 7 + B2 = 17 + B Solving for variable 'B'. Reorder the terms: 7 + -17 + -1B + B2 = 17 + B + -17 + -1B Combine like terms: 7 + -17 = -10 -10 + -1B + B2 = 17 + B + -17 + -1B Reorder the terms: -10 + -1B + B2 = 17 + -17 + B + -1B Combine like terms: 17 + -17 = 0 -10 + -1B + B2 = 0 + B + -1B -10 + -1B + B2 = B + -1B Combine like terms: B + -1B = 0 -10 + -1B + B2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -1B + 10 + B2 = 0 + 10 Reorder the terms: -10 + 10 + -1B + B2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1B + B2 = 0 + 10 -1B + B2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1B + B2 = 10 The B term is -1B. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1B + 0.25 + B2 = 10 + 0.25 Reorder the terms: 0.25 + -1B + B2 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + -1B + B2 = 10.25 Factor a perfect square on the left side: (B + -0.5)(B + -0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (B + -0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
B + -0.5 = 3.201562119 Simplifying B + -0.5 = 3.201562119 Reorder the terms: -0.5 + B = 3.201562119 Solving -0.5 + B = 3.201562119 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + B = 3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + B = 3.201562119 + 0.5 B = 3.201562119 + 0.5 Combine like terms: 3.201562119 + 0.5 = 3.701562119 B = 3.701562119 Simplifying B = 3.701562119Subproblem 2
B + -0.5 = -3.201562119 Simplifying B + -0.5 = -3.201562119 Reorder the terms: -0.5 + B = -3.201562119 Solving -0.5 + B = -3.201562119 Solving for variable 'B'. Move all terms containing B to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + B = -3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + B = -3.201562119 + 0.5 B = -3.201562119 + 0.5 Combine like terms: -3.201562119 + 0.5 = -2.701562119 B = -2.701562119 Simplifying B = -2.701562119Solution
The solution to the problem is based on the solutions from the subproblems. B = {3.701562119, -2.701562119}
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