5n^2-10n+10=0

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Solution for 5n^2-10n+10=0 equation:


Simplifying
5n2 + -10n + 10 = 0

Reorder the terms:
10 + -10n + 5n2 = 0

Solving
10 + -10n + 5n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -2n + n2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(2 + -2n + n2)' equal to zero and attempt to solve: Simplifying 2 + -2n + n2 = 0 Solving 2 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -2n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2n + n2 = 0 + -2 -2n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2n + n2 = -2 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = -2 + 1 Reorder the terms: 1 + -2n + n2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2n + n2 = -1 Factor a perfect square on the left side: (n + -1)(n + -1) = -1 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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