Question

I need to find both of the solutions to the equation 100+(n-2)^ = 149

Answer 1

Answer:

Step-by-step explanation:

hello :

100+(n-2)² = 149

100-100+(n-2)² = 149-100

(n-2)² = 49  

(n-2)² - 49  =0    but 49=7²

(n-2)² - 7²  =0   use identity : a²-b²=(a-b)(a+b)

(n-2-7)(n-2+7)=0

(n-9)(n+5)=0

n-9=0 or n+5=0

n=9 or n=-5

                                             

Answer 2

The solutions of the given equation are -5 and 9

The given equation:

$100 + (n-2)^2 = 149$

To find:

• the solutions of n

The solutions of n are obtained by expanding the given equation;

$100 + (n-2)^2 = 149\\\\100 + n^2 - 4n+ 4 = 149\\\\collect \ similar \ terms \ together\\\\(100 + 4 -149) + n^2-4n = 0\\\\-45 + n^2 -4n = 0\\\\rearrange \ the \ equation \ as \ follows\\\\n^2 - 4n - 45= 0\\\\factorize \ the \ quadratic \ equation \ as \ follows\\\\n^2 +5n -9n -45=0\\\\n(n+5) -9(n + 5) =0\\\\(n+5)(n-9)=0\\\\n = -5 \ \ \ or \ \ \ \ \ 9$

Thus, the solutions of the given equation are -5 and 9

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