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Simplifying 9f2 + 18f + 45 = 0 Reorder the terms: 45 + 18f + 9f2 = 0 Solving 45 + 18f + 9f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '9'. 9(5 + 2f + f2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(5 + 2f + f2)' equal to zero and attempt to solve: Simplifying 5 + 2f + f2 = 0 Solving 5 + 2f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 2f + -5 + f2 = 0 + -5 Reorder the terms: 5 + -5 + 2f + f2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2f + f2 = 0 + -5 2f + f2 = 0 + -5 Combine like terms: 0 + -5 = -5 2f + f2 = -5 The f term is 2f. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2f + 1 + f2 = -5 + 1 Reorder the terms: 1 + 2f + f2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + 2f + f2 = -4 Factor a perfect square on the left side: (f + 1)(f + 1) = -4 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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