2n^2=10+n

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Solution for 2n^2=10+n equation:


Simplifying
2n2 = 10 + n

Solving
2n2 = 10 + n

Solving for variable 'n'.

Reorder the terms:
-10 + -1n + 2n2 = 10 + n + -10 + -1n

Reorder the terms:
-10 + -1n + 2n2 = 10 + -10 + n + -1n

Combine like terms: 10 + -10 = 0
-10 + -1n + 2n2 = 0 + n + -1n
-10 + -1n + 2n2 = n + -1n

Combine like terms: n + -1n = 0
-10 + -1n + 2n2 = 0

Factor a trinomial.
(-2 + -1n)(5 + -2n) = 0

Subproblem 1

Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2

Subproblem 2

Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5

Solution

n = {-2, 2.5}

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