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Simplifying b2 + 4b + -7 = 0 Reorder the terms: -7 + 4b + b2 = 0 Solving -7 + 4b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 4b + 7 + b2 = 0 + 7 Reorder the terms: -7 + 7 + 4b + b2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4b + b2 = 0 + 7 4b + b2 = 0 + 7 Combine like terms: 0 + 7 = 7 4b + b2 = 7 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 = 7 + 4 Reorder the terms: 4 + 4b + b2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + 4b + b2 = 11 Factor a perfect square on the left side: (b + 2)(b + 2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (b + 2) equal to 3.31662479 and -3.31662479.Subproblem 1
b + 2 = 3.31662479 Simplifying b + 2 = 3.31662479 Reorder the terms: 2 + b = 3.31662479 Solving 2 + b = 3.31662479 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 = 3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + b = 3.31662479 + -2 b = 3.31662479 + -2 Combine like terms: 3.31662479 + -2 = 1.31662479 b = 1.31662479 Simplifying b = 1.31662479Subproblem 2
b + 2 = -3.31662479 Simplifying b + 2 = -3.31662479 Reorder the terms: 2 + b = -3.31662479 Solving 2 + b = -3.31662479 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 = -3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + b = -3.31662479 + -2 b = -3.31662479 + -2 Combine like terms: -3.31662479 + -2 = -5.31662479 b = -5.31662479 Simplifying b = -5.31662479Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.31662479, -5.31662479}
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