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Simplifying 8b2 + -32b + -16 = 0 Reorder the terms: -16 + -32b + 8b2 = 0 Solving -16 + -32b + 8b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + -4b + b2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -4b + b2)' equal to zero and attempt to solve: Simplifying -2 + -4b + b2 = 0 Solving -2 + -4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -4b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4b + b2 = 0 + 2 -4b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4b + b2 = 2 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 = 2 + 4 Reorder the terms: 4 + -4b + b2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4b + b2 = 6 Factor a perfect square on the left side: (b + -2)(b + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (b + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
b + -2 = 2.449489743 Simplifying b + -2 = 2.449489743 Reorder the terms: -2 + b = 2.449489743 Solving -2 + b = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + b = 2.449489743 + 2 b = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 b = 4.449489743 Simplifying b = 4.449489743Subproblem 2
b + -2 = -2.449489743 Simplifying b + -2 = -2.449489743 Reorder the terms: -2 + b = -2.449489743 Solving -2 + b = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + b = -2.449489743 + 2 b = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 b = -0.449489743 Simplifying b = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.449489743, -0.449489743}Solution
b = {4.449489743, -0.449489743}
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