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Simplifying 6b2 + -54b + -72 = 0 Reorder the terms: -72 + -54b + 6b2 = 0 Solving -72 + -54b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '6'. 6(-12 + -9b + b2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-12 + -9b + b2)' equal to zero and attempt to solve: Simplifying -12 + -9b + b2 = 0 Solving -12 + -9b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -9b + 12 + b2 = 0 + 12 Reorder the terms: -12 + 12 + -9b + b2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -9b + b2 = 0 + 12 -9b + b2 = 0 + 12 Combine like terms: 0 + 12 = 12 -9b + b2 = 12 The b term is -9b. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9b + 20.25 + b2 = 12 + 20.25 Reorder the terms: 20.25 + -9b + b2 = 12 + 20.25 Combine like terms: 12 + 20.25 = 32.25 20.25 + -9b + b2 = 32.25 Factor a perfect square on the left side: (b + -4.5)(b + -4.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (b + -4.5) equal to 5.678908346 and -5.678908346.Subproblem 1
b + -4.5 = 5.678908346 Simplifying b + -4.5 = 5.678908346 Reorder the terms: -4.5 + b = 5.678908346 Solving -4.5 + b = 5.678908346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + b = 5.678908346 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + b = 5.678908346 + 4.5 b = 5.678908346 + 4.5 Combine like terms: 5.678908346 + 4.5 = 10.178908346 b = 10.178908346 Simplifying b = 10.178908346Subproblem 2
b + -4.5 = -5.678908346 Simplifying b + -4.5 = -5.678908346 Reorder the terms: -4.5 + b = -5.678908346 Solving -4.5 + b = -5.678908346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + b = -5.678908346 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + b = -5.678908346 + 4.5 b = -5.678908346 + 4.5 Combine like terms: -5.678908346 + 4.5 = -1.178908346 b = -1.178908346 Simplifying b = -1.178908346Solution
The solution to the problem is based on the solutions from the subproblems. b = {10.178908346, -1.178908346}Solution
b = {10.178908346, -1.178908346}
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