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Simplifying 2b2 + -8b + -8 = 0 Reorder the terms: -8 + -8b + 2b2 = 0 Solving -8 + -8b + 2b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -4b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -4b + b2)' equal to zero and attempt to solve: Simplifying -4 + -4b + b2 = 0 Solving -4 + -4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -4b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + -4b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4b + b2 = 0 + 4 -4b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4b + b2 = 4 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 = 4 + 4 Reorder the terms: 4 + -4b + b2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4b + b2 = 8 Factor a perfect square on the left side: (b + -2)(b + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (b + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
b + -2 = 2.828427125 Simplifying b + -2 = 2.828427125 Reorder the terms: -2 + b = 2.828427125 Solving -2 + b = 2.828427125 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 = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + b = 2.828427125 + 2 b = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 b = 4.828427125 Simplifying b = 4.828427125Subproblem 2
b + -2 = -2.828427125 Simplifying b + -2 = -2.828427125 Reorder the terms: -2 + b = -2.828427125 Solving -2 + b = -2.828427125 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 = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + b = -2.828427125 + 2 b = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 b = -0.828427125 Simplifying b = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.828427125, -0.828427125}Solution
b = {4.828427125, -0.828427125}
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