2n^2=-7n+99

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Solution for 2n^2=-7n+99 equation:


Simplifying
2n2 = -7n + 99

Reorder the terms:
2n2 = 99 + -7n

Solving
2n2 = 99 + -7n

Solving for variable 'n'.

Reorder the terms:
-99 + 7n + 2n2 = 99 + -7n + -99 + 7n

Reorder the terms:
-99 + 7n + 2n2 = 99 + -99 + -7n + 7n

Combine like terms: 99 + -99 = 0
-99 + 7n + 2n2 = 0 + -7n + 7n
-99 + 7n + 2n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-99 + 7n + 2n2 = 0

Factor a trinomial.
(-9 + -1n)(11 + -2n) = 0

Subproblem 1

Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9

Subproblem 2

Set the factor '(11 + -2n)' equal to zero and attempt to solve: Simplifying 11 + -2n = 0 Solving 11 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2n = 0 + -11 -2n = 0 + -11 Combine like terms: 0 + -11 = -11 -2n = -11 Divide each side by '-2'. n = 5.5 Simplifying n = 5.5

Solution

n = {-9, 5.5}

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