stewbug97
Answered

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Solve for x.

(x−2)^2+2=38

x= ___ or x= ___

Sagot :

MissSpanish

Answer:

[tex]x \: = \: \boxed{ \bold{ - 4 }}\: \: \text{or} \: \: x \: = \: \boxed{ \bold{ 8}}[/tex]

Step-by-step explanation:

[tex](x \: - \: 2 {)}^{2} \: + \: 2 \: = \: 38[/tex]

[tex] {x}^{2} \: - \: 4x \: + \: 4 \: + \: 2 \: = \: 38[/tex]

[tex] {x}^{2} \: - \: 4x \: + \: 6 \: = \: 38[/tex]

[tex] {x}^{2} \: - \: 4x \: + \: 6 \: - \: 38 \: = \: 0[/tex]

[tex] {x}^{2} \: + \: 4x \: - \: 8x \: - \: 32 \: = \: 0[/tex]

[tex]x \: \times \: (x \: + \: 4) \: - \: 8(x \: + \: 4) \: = \: 0[/tex]

[tex](x \: + \: 4) \: \times \: (x \: - \: 8) \: = \: 0[/tex]

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

[tex]x \: + \: 4 \: = \: 0 \\ x \: - \: 8 \: = \: 0[/tex]

  • We solve the two equations:

[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]

Answer:

[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]

MissSpanish

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