What are the solutions to the equation (n(n+1))/2 =575 ?

The solutions to the equation (n(n+1))/2 =575 are n=(-1+sqrt(4601))/2 ,n=(-1-sqrt(4601))/2

Find the zeros of (n(n+1))/2 =575

The zeros of (n(n+1))/2 =575 are n=(-1+sqrt(4601))/2 ,n=(-1-sqrt(4601))/2

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\frac{n ( n + 1 )}{2} = 575

n = \frac{- 1 + 4601}{2}, n = \frac{- 1 - 4601}{2}

Decimal Notation

n = 33.41533 \dots, n = - 34.41533 \dots

Solution steps

\frac{n ( n + 1 )}{2} = 575

Multiply both sides by

2

n (n + 1) = 1150

Expand

n (n + 1) : n^{2} + n

n^{2} + n = 1150

Move

1150

to the left side

n^{2} + n - 1150 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 1150 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 1150) = 4601

n_{1, 2} = \frac{- 1 \pm 4601}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- 1 + 4601}{2 \cdot 1}, n_{2} = \frac{- 1 - 4601}{2 \cdot 1}

n = \frac{- 1 + 4601}{2 \cdot 1} : \frac{- 1 + 4601}{2}

n = \frac{- 1 - 4601}{2 \cdot 1} : \frac{- 1 - 4601}{2}

The solutions to the quadratic equation are:

n = \frac{- 1 + 4601}{2}, n = \frac{- 1 - 4601}{2}

x^{2} - 8 x + c

3 x^{2} - 9 x + 4 = 0

\frac{3 ( x ^{2} + 6 )}{2} = 1

4 x^{2} + 16 x + 1 = 0

(1 - 3) x^{2} + 3 x - 4 = 0

What are the solutions to the equation (n(n+1))/2 =575 ?
The solutions to the equation (n(n+1))/2 =575 are n=(-1+sqrt(4601))/2 ,n=(-1-sqrt(4601))/2
Find the zeros of (n(n+1))/2 =575
The zeros of (n(n+1))/2 =575 are n=(-1+sqrt(4601))/2 ,n=(-1-sqrt(4601))/2