Question 1

Solve for x.

(x−2)^2+2=38

x= ___ or x= ___

Question 2

Answer:

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

Explanation:

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

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

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

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

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

$x \: * \: (x \: + \: 4) \: - \: 8(x \: + \: 4) \: = \: 0$

$(x \: + \: 4) \: * \: (x \: - \: 8) \: = \: 0$

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

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

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

Answer:

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

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