Rewrite \(x^2+2x-5\) in the form \((x+p)^2+q\).
\((x+1)^2-6\)
\((x+1)^2+6\)
\((x-1)^2-6\)
\((x+2)^2-9\)
Complete the square:
\(x^2+2x-5=(x+1)^2-1-5=(x+1)^2-6\).
Rewrite \(x^2-10x+20\) in the form \((x+p)^2+q\).
\((x-5)^2+5\)
\((x-5)^2-5\)
\((x-10)^2-80\)
\((x+5)^2-5\)
\(x^2-10x+20=(x-5)^2-25+20=(x-5)^2-5\).
Rewrite \(x^2-4x+1\) in the form \((x+p)^2+q\).
\((x-2)^2-3\)
\((x-4)^2-15\)
\((x+2)^2-3\)
\((x-2)^2+3\)
\(x^2-4x+1=(x-2)^2-4+1=(x-2)^2-3\).
Rewrite \(6-8x-x^2\) in the form \(q-(x+p)^2\).
\(22-(x-4)^2\)
\(22-(x+4)^2\)
\((x+4)^2-22\)
\(6-(x+4)^2\)
Factor out the negative sign from the quadratic part:
\(6-8x-x^2=-(x^2+8x)+6\).
Complete the square inside:
\(x^2+8x=(x+4)^2-16\).
So
\(6-8x-x^2=-[(x+4)^2-16]+6=22-(x+4)^2\).
Rewrite \(10-16x-x^2\) in the form \(q-(x+p)^2\).
\(74-(x-8)^2\)
\(10-(x+8)^2\)
\((x+8)^2-74\)
\(74-(x+8)^2\)
\(10-16x-x^2=-(x^2+16x)+10\).
Now
\(x^2+16x=(x+8)^2-64\).
\(10-16x-x^2=-[(x+8)^2-64]+10=74-(x+8)^2\).