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Simplifying 6b2 + -24b + -54 = 0 Reorder the terms: -54 + -24b + 6b2 = 0 Solving -54 + -24b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + -4b + b2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -4b + b2)' equal to zero and attempt to solve: Simplifying -9 + -4b + b2 = 0 Solving -9 + -4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4b + 9 + b2 = 0 + 9 Reorder the terms: -9 + 9 + -4b + b2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4b + b2 = 0 + 9 -4b + b2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4b + b2 = 9 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 = 9 + 4 Reorder the terms: 4 + -4b + b2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4b + b2 = 13 Factor a perfect square on the left side: (b + -2)(b + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (b + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
b + -2 = 3.605551275 Simplifying b + -2 = 3.605551275 Reorder the terms: -2 + b = 3.605551275 Solving -2 + b = 3.605551275 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 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + b = 3.605551275 + 2 b = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 b = 5.605551275 Simplifying b = 5.605551275Subproblem 2
b + -2 = -3.605551275 Simplifying b + -2 = -3.605551275 Reorder the terms: -2 + b = -3.605551275 Solving -2 + b = -3.605551275 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 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + b = -3.605551275 + 2 b = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 b = -1.605551275 Simplifying b = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.605551275, -1.605551275}Solution
b = {5.605551275, -1.605551275}
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