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sweet [91]
2 years ago
7

Solve for x. (x−2)^2+2=38 x= ___ or x= ___

Mathematics
1 answer:
Elan Coil [88]2 years ago
6 0

Answer:

x  \: = \:  \boxed{ \bold{  - 4  }}\:    \:    \text{or} \:   \: x \:  = \:  \boxed{ \bold{ 8}}

Step-by-step explanation:

(x \:  -  \: 2 {)}^{2}  \:  +  \: 2 \:  =  \: 38

{x}^{2}  \:  -  \: 4x \:  +  \: 4 \:  +  \: 2 \:  =  \: 38

{x}^{2}  \:  -  \: 4x \:  +  \: 6 \:  =  \: 38

{x}^{2}  \:  -  \: 4x \:  +  \: 6 \:  -  \: 38 \:  =  \: 0

{x}^{2}  \:  +  \: 4x \:  -  \: 8x \:  -  \: 32 \:  =  \: 0

x \:  \times  \: (x \:  +  \: 4) \:  -  \: 8(x \:  +  \: 4) \:  =  \: 0

(x \:  +  \: 4) \:   \times  \: (x \:  -  \: 8) \:  =  \: 0

  • When it happens that the product of the factors is the same as zero. It is divided into two possible cases.

x \:  +  \: 4 \:  =  \: 0 \\ x \:  -  \: 8 \:  =  \: 0

  • We solve the two equations:

x \:  =  \:  - 4 \\ x \:  =  \: 8

<h2>Answer: </h2>

x \:  =  \:  - 4 \\ x \:  =  \: 8

<h3><em><u>MissSpanish</u></em></h3>

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