Question

210=n(n+1)/2

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Answer 1

step-by-step explanation

Simplifying

n(n + 1) = 210

Reorder the terms:

n(1 + n) = 210

(1 * n + n * n) = 210

(1n + n2) = 210

Solving

1n + n2 = 210

Solving for variable 'n'.

Reorder the terms:

-210 + 1n + n2 = 210 + -210

Combine like terms: 210 + -210 = 0

-210 + 1n + n2 = 0

Factor a trinomial.

(-15 + -1n)(14 + -1n) = 0

Subproblem 1

Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying

-15 + -1n = 0

Solving

-15 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0

0 + -1n = 0 + 15

-1n = 0 + 15

Combine like terms: 0 + 15 = 15

-1n = 15

Divide each side by '-1'.

n = -15

Simplifying

n = -15

Subproblem 2

Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying

14 + -1n = 0

Solving

14 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-14' to each side of the equation.

14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0

0 + -1n = 0 + -14

-1n = 0 + -14

Combine like terms: 0 + -14 = -14

-1n = -14

Divide each side by '-1'.

n = 14

Simplifying

n = 14

Solution

n = {-15, 14}

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