Gleichungen mit binomischen Formeln: (x-8)^2 -60 = (x+5)^2 + 5

Question

(x-8)zum quadrat -60=(x+5)zum quadrat+5

Answer 1

(x-8)^2 -60 = (x+5)^2 + 5

x^2 - 16x + 64 - 60 = x^2 + 10x + 25 + 5       | -x^2

-16x + 4 = 10x + 30

Soweit klar? Kommst du nun selbst zu x?

-16x + 4 = 10x + 30           | + 16x -30

-26 = 26x     |:26

-1 = x

Probe:

(-1-8)^2 -60 =?= (-1+5)^2 + 5 

81 - 60 =?= 16 + 5 

21 = 21

stimmt. 

Answer 2

(x-8)² -60 = (x+5)² + 5

x^2-16 x +64 -60=x^2+10x +25 +5

x^2-16 x +4 =x^2+10x +30 | -x^2

-16 x +4 =10x +30| -4

-16x = 10x +26 |-10x

-26x= 26

x= -1

Answer 3

$$ \begin{aligned} (x-8)^2 - 60 &= (x+5)^2 + 5 \\\,\\(x-8)^2 - (x+5)^2 &=  65 \\\,\\\left((x-8) - (x+5)\right) \cdot \left((x-8) + (x+5)\right) &=  65 \\\,\\-13 \cdot \left( 2x-3 \right) &=  65 \\\,\\2x-3 &=  -5 \\\,\\2x &=  -2 \\\,\\x &=  -1\end{aligned} $$