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Simplifying 2b2 + -16b + 16 = 0 Reorder the terms: 16 + -16b + 2b2 = 0 Solving 16 + -16b + 2b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -8b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -8b + b2)' equal to zero and attempt to solve: Simplifying 8 + -8b + b2 = 0 Solving 8 + -8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8b + -8 + b2 = 0 + -8 Reorder the terms: 8 + -8 + -8b + b2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8b + b2 = 0 + -8 -8b + b2 = 0 + -8 Combine like terms: 0 + -8 = -8 -8b + b2 = -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 = -8 + 16 Reorder the terms: 16 + -8b + b2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8b + b2 = 8 Factor a perfect square on the left side: (b + -4)(b + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (b + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
b + -4 = 2.828427125 Simplifying b + -4 = 2.828427125 Reorder the terms: -4 + b = 2.828427125 Solving -4 + b = 2.828427125 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 = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + b = 2.828427125 + 4 b = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 b = 6.828427125 Simplifying b = 6.828427125Subproblem 2
b + -4 = -2.828427125 Simplifying b + -4 = -2.828427125 Reorder the terms: -4 + b = -2.828427125 Solving -4 + b = -2.828427125 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 = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + b = -2.828427125 + 4 b = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 b = 1.171572875 Simplifying b = 1.171572875Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.828427125, 1.171572875}Solution
b = {6.828427125, 1.171572875}
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