Answer:
[tex](x-3)^2=5[/tex]
Step-by-step explanation:
[tex]x^2-4x+4=2x[/tex]
[tex]x^2-4x+4-2x=2x-2x[/tex]
[tex]x^2-6x+4=0[/tex]
[tex]x^2-6x=-4[/tex]
[tex]x^2-6x+9=-4+9[/tex]
[tex](x-3)^2=5[/tex]
Solving:
[tex]x-3=\pm \sqrt{5}[/tex]
[tex]x=3 \pm \sqrt{5}[/tex]
An equation is formed when two equal expressions. The equation by completing the square can be rewritten as (x-3)²=5.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be rewritten in the equation form by completing the square as,
x² - 4x + 4 = 2x
Bring the like terms on the same side of the equation,
x² - 4x - 2x + 4 = 0
Simplify the like terms of the equation,
x² - 6x + 4 = 0
Add positive 5 to both sides of the equation,
x² - 6x + 4 + 5 = 5
Solve the like terms,
x² - 6x + 9 = 5
Using the binomial property (a-b)²=a²+b²-2ab, x² - 6x + 9 can be written as,
(x - 3)² = 5
Hence, the equation by completing the square can be rewritten as (x-3)²=5.
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