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Simplifying 6b2 + 36b + 378 = 0 Reorder the terms: 378 + 36b + 6b2 = 0 Solving 378 + 36b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '6'. 6(63 + 6b + b2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(63 + 6b + b2)' equal to zero and attempt to solve: Simplifying 63 + 6b + b2 = 0 Solving 63 + 6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 6b + -63 + b2 = 0 + -63 Reorder the terms: 63 + -63 + 6b + b2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 6b + b2 = 0 + -63 6b + b2 = 0 + -63 Combine like terms: 0 + -63 = -63 6b + b2 = -63 The b term is 6b. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6b + 9 + b2 = -63 + 9 Reorder the terms: 9 + 6b + b2 = -63 + 9 Combine like terms: -63 + 9 = -54 9 + 6b + b2 = -54 Factor a perfect square on the left side: (b + 3)(b + 3) = -54 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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