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Simplifying 6f2 + 3 + -4f + 5 + 10f2 = 0 Reorder the terms: 3 + 5 + -4f + 6f2 + 10f2 = 0 Combine like terms: 3 + 5 = 8 8 + -4f + 6f2 + 10f2 = 0 Combine like terms: 6f2 + 10f2 = 16f2 8 + -4f + 16f2 = 0 Solving 8 + -4f + 16f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -1f + 4f2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -1f + 4f2)' equal to zero and attempt to solve: Simplifying 2 + -1f + 4f2 = 0 Solving 2 + -1f + 4f2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -0.25f + f2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.25f + -0.5 + f2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.25f + f2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.25f + f2 = 0 + -0.5 -0.25f + f2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.25f + f2 = -0.5 The f term is -0.25f. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25f + 0.015625 + f2 = -0.5 + 0.015625 Reorder the terms: 0.015625 + -0.25f + f2 = -0.5 + 0.015625 Combine like terms: -0.5 + 0.015625 = -0.484375 0.015625 + -0.25f + f2 = -0.484375 Factor a perfect square on the left side: (f + -0.125)(f + -0.125) = -0.484375 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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