8n^2-4n+6=0

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Solution for 8n^2-4n+6=0 equation:


Simplifying
8n2 + -4n + 6 = 0

Reorder the terms:
6 + -4n + 8n2 = 0

Solving
6 + -4n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2n + 4n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -2n + 4n2)' equal to zero and attempt to solve: Simplifying 3 + -2n + 4n2 = 0 Solving 3 + -2n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -0.5n + n2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.5n + -0.75 + n2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.5n + n2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.5n + n2 = 0 + -0.75 -0.5n + n2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.5n + n2 = -0.75 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + -0.5n + n2 = -0.6875 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = -0.6875 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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