Question

2x^2-1x+1 factor please help

Answer 1

\[2x ^{2}-1x+1=2\left( x ^{2}-\frac{ 1 }{2 }x \right)+1\]
\[=2\left( x ^{2}-\frac{ 1 }{ 2 }x+\frac{ 1 }{ 16 }-\frac{ 1 }{ 16 } \right)+1\]
\[=2\left( x-\frac{ 1 }{ 4 } \right)^{2}-\frac{ 2 }{16 }+1\]
\[=2\left( x-\frac{ 1 }{ 4 } \right)^{2}+\frac{ 14 }{ 16 }\]
\[=2\left[ \left( x-\frac{ 1 }{ 4 } \right) ^{2}-\left( \frac{ -\sqrt{7} }{4 } \right)^{2}\right]\]
\[=2\left[ \left( x-\frac{ 1 }{4} \right)^{2} -\left( \frac{ \iota \sqrt{7} }{4 } \right)^{2}\right]\]
\[=2\left(x-\frac{ 1 }{ 4 } +\frac{ \iota \sqrt{7} }{ 4}\right)\left( x-\frac{ 1 }{ 4 }-\frac{ \iota \sqrt{7} }{ 4} \right)\]