(8n)(8n)+4=12n

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Solution for (8n)(8n)+4=12n equation:


Simplifying
(8n)(8n) + 4 = 12n

Remove parenthesis around (8n)
8n(8n) + 4 = 12n

Remove parenthesis around (8n)
8n * 8n + 4 = 12n

Reorder the terms for easier multiplication:
8 * 8n * n + 4 = 12n

Multiply 8 * 8
64n * n + 4 = 12n

Multiply n * n
64n2 + 4 = 12n

Reorder the terms:
4 + 64n2 = 12n

Solving
4 + 64n2 = 12n

Solving for variable 'n'.

Reorder the terms:
4 + -12n + 64n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
4 + -12n + 64n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -3n + 16n2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(1 + -3n + 16n2)' equal to zero and attempt to solve: Simplifying 1 + -3n + 16n2 = 0 Solving 1 + -3n + 16n2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -0.1875n + n2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.1875n + -0.0625 + n2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.1875n + n2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.1875n + n2 = 0 + -0.0625 -0.1875n + n2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.1875n + n2 = -0.0625 The n term is -0.1875n. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875n + 0.0087890625 + n2 = -0.0625 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875n + n2 = -0.0625 + 0.0087890625 Combine like terms: -0.0625 + 0.0087890625 = -0.0537109375 0.0087890625 + -0.1875n + n2 = -0.0537109375 Factor a perfect square on the left side: (n + -0.09375)(n + -0.09375) = -0.0537109375 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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