Stewbug97idn
Answered

Explore IDNLearn.com to discover insightful answers from experts and enthusiasts alike. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.

Solve for x.

(x−2)^2+2=38

x= ___ or x= ___

Sagot :

MissSpanishidn

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

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.