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Simplifying b2 + -20b + 57 = 7 Reorder the terms: 57 + -20b + b2 = 7 Solving 57 + -20b + b2 = 7 Solving for variable 'b'. Reorder the terms: 57 + -7 + -20b + b2 = 7 + -7 Combine like terms: 57 + -7 = 50 50 + -20b + b2 = 7 + -7 Combine like terms: 7 + -7 = 0 50 + -20b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -20b + -50 + b2 = 0 + -50 Reorder the terms: 50 + -50 + -20b + b2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -20b + b2 = 0 + -50 -20b + b2 = 0 + -50 Combine like terms: 0 + -50 = -50 -20b + b2 = -50 The b term is -20b. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20b + 100 + b2 = -50 + 100 Reorder the terms: 100 + -20b + b2 = -50 + 100 Combine like terms: -50 + 100 = 50 100 + -20b + b2 = 50 Factor a perfect square on the left side: (b + -10)(b + -10) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (b + -10) equal to 7.071067812 and -7.071067812.Subproblem 1
b + -10 = 7.071067812 Simplifying b + -10 = 7.071067812 Reorder the terms: -10 + b = 7.071067812 Solving -10 + b = 7.071067812 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + b = 7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + b = 7.071067812 + 10 b = 7.071067812 + 10 Combine like terms: 7.071067812 + 10 = 17.071067812 b = 17.071067812 Simplifying b = 17.071067812Subproblem 2
b + -10 = -7.071067812 Simplifying b + -10 = -7.071067812 Reorder the terms: -10 + b = -7.071067812 Solving -10 + b = -7.071067812 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + b = -7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + b = -7.071067812 + 10 b = -7.071067812 + 10 Combine like terms: -7.071067812 + 10 = 2.928932188 b = 2.928932188 Simplifying b = 2.928932188Solution
The solution to the problem is based on the solutions from the subproblems. b = {17.071067812, 2.928932188}
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