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Simplifying b2 + -8b + 7.8 = 0 Reorder the terms: 7.8 + -8b + b2 = 0 Solving 7.8 + -8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-7.8' to each side of the equation. 7.8 + -8b + -7.8 + b2 = 0 + -7.8 Reorder the terms: 7.8 + -7.8 + -8b + b2 = 0 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + -8b + b2 = 0 + -7.8 -8b + b2 = 0 + -7.8 Combine like terms: 0 + -7.8 = -7.8 -8b + b2 = -7.8 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = -7.8 + 16 Reorder the terms: 16 + -8b + b2 = -7.8 + 16 Combine like terms: -7.8 + 16 = 8.2 16 + -8b + b2 = 8.2 Factor a perfect square on the left side: (b + -4)(b + -4) = 8.2 Calculate the square root of the right side: 2.863564213 Break this problem into two subproblems by setting (b + -4) equal to 2.863564213 and -2.863564213.Subproblem 1
b + -4 = 2.863564213 Simplifying b + -4 = 2.863564213 Reorder the terms: -4 + b = 2.863564213 Solving -4 + b = 2.863564213 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 2.863564213 + 4 Combine like terms: -4 + 4 = 0 0 + b = 2.863564213 + 4 b = 2.863564213 + 4 Combine like terms: 2.863564213 + 4 = 6.863564213 b = 6.863564213 Simplifying b = 6.863564213Subproblem 2
b + -4 = -2.863564213 Simplifying b + -4 = -2.863564213 Reorder the terms: -4 + b = -2.863564213 Solving -4 + b = -2.863564213 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -2.863564213 + 4 Combine like terms: -4 + 4 = 0 0 + b = -2.863564213 + 4 b = -2.863564213 + 4 Combine like terms: -2.863564213 + 4 = 1.136435787 b = 1.136435787 Simplifying b = 1.136435787Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.863564213, 1.136435787}
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