Question

solve the equation 78=2+(n-1)2​

Answer 1

Answer:

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Step-by-step explanation:

n(n-1)/2=78

We move all terms to the left:

n(n-1)/2-(78)=0

We multiply all the terms by the denominator

n(n-1)-78*2=0

We add all the numbers together, and all the variables

n(n-1)-156=0

We multiply parentheses

n^2-1n-156=0

a = 1; b = -1; c = -156;

Δ = b2-4ac

Δ = -12-4·1·(-156)

Δ = 625

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

n1=−b−Δ√2an2=−b+Δ√2a

Δ−−√=625−−−√=25

n1=−b−Δ√2a=−(−1)−252∗1=−242=−12

n2=−b+Δ√2a=−(−1)+252∗1=262=13

Answer 2

78=2+2n-2

2n=2-2-78

2n=2-80

2n=-78

n= -78/2

n= -39