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root of negative 2x plus 1 _ 3 = x

Square root of negative 2x plus 1 _ 3 + 3 = x + 3

Square root of negative 2x plus 1 = x + 3

Square root of negative 2x plus 1 _ 1 = x + 3 _ 1

Square root of negative 2 x = x + 2

(Square root of negative 2 x)2 = (x _ 4)2

_2x = x2 _ 8x + 16

_2x + 2x = x2 + 8x + 16 + 2x

0 = x2 + 10x + 16

0 = (x + 2)(x + 8)


x + 2 = 0 x + 8 = 0

x + 2 _ 2 = 0 _ 2 x + 8 _ 8 = 0

Verified Answer :

The following errors are made:

\(\sqrt{-2x+1}-1=x+3-1 \\ \sqrt{-2x} =x+2\) - cannot subtract 1 from radical

\(\sqrt{-2x} =x+2\\ \sqrt{-2x}^2 =(x-4)^2\) - (x+2) should be squared

\(0=x^2+8x+16 \\0=(x+2)(x+6)\) - incorrect factoring

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