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Simplifying b2 + 7b = 56 Reorder the terms: 7b + b2 = 56 Solving 7b + b2 = 56 Solving for variable 'b'. Reorder the terms: -56 + 7b + b2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 7b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 7b + 56 + b2 = 0 + 56 Reorder the terms: -56 + 56 + 7b + b2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 7b + b2 = 0 + 56 7b + b2 = 0 + 56 Combine like terms: 0 + 56 = 56 7b + b2 = 56 The b term is 7b. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7b + 12.25 + b2 = 56 + 12.25 Reorder the terms: 12.25 + 7b + b2 = 56 + 12.25 Combine like terms: 56 + 12.25 = 68.25 12.25 + 7b + b2 = 68.25 Factor a perfect square on the left side: (b + 3.5)(b + 3.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (b + 3.5) equal to 8.261355821 and -8.261355821.Subproblem 1
b + 3.5 = 8.261355821 Simplifying b + 3.5 = 8.261355821 Reorder the terms: 3.5 + b = 8.261355821 Solving 3.5 + b = 8.261355821 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = 8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = 8.261355821 + -3.5 b = 8.261355821 + -3.5 Combine like terms: 8.261355821 + -3.5 = 4.761355821 b = 4.761355821 Simplifying b = 4.761355821Subproblem 2
b + 3.5 = -8.261355821 Simplifying b + 3.5 = -8.261355821 Reorder the terms: 3.5 + b = -8.261355821 Solving 3.5 + b = -8.261355821 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = -8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = -8.261355821 + -3.5 b = -8.261355821 + -3.5 Combine like terms: -8.261355821 + -3.5 = -11.761355821 b = -11.761355821 Simplifying b = -11.761355821Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.761355821, -11.761355821}
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