IDislikeAlgebra
Answered

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(x-2)^2-6(x-2)+5=0
Find a Value of X

Sagot :

absor201

Answer:

The values of x are:

[tex]x=3,\:x=7[/tex]

Step-by-step explanation:

Given the expression

[tex](x-2)^2-6(x-2)+5=0[/tex]

Expand (x - 2)² = x² -4x + 4

[tex]x^2-4x+4-6\left(x-2\right)+5=0[/tex]

Expand: -6(x - 2) = -6x + 12

[tex]x^2-4x+4-6x+12+5=0[/tex]

simplifying

[tex]x^2-10x+21=0[/tex]

Factor  x² -10x + 21:  (x - 3) (x - 7)

[tex]\left(x-3\right)\left(x-7\right)=0[/tex]

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

[tex]x-3=0\quad \mathrm{or}\quad \:x-7=0[/tex]

solving x - 3 = 0

x - 3 = 0

Adding 3 to both sides

[tex]x-3+3=0+3[/tex]

simplify

x = 3

solving x - 7 = 0

x - 7 = 0

Adding 7 to both sides

[tex]x-7+7=0+7[/tex]

Simplify

x = 7

Therefore, the values of x are:

[tex]x=3,\:x=7[/tex]

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