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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 = 5.31662479 b = 5.31662479 Simplifying b = 5.31662479Subproblem 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 = -1.31662479 b = -1.31662479 Simplifying b = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.31662479, -1.31662479}
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