Question 1133750
{{{(X-4)^5 -7(X-4)^4 +7(X-4)^3 -7(X-4)^2 +7(X-4)-6=0}}}

first expand:

{{{(X-4)^5=(X-4)(X-4)(X-4)(X-4)(X-4)=X^5 - 20 X^4 + 160 X^3 - 640 X^2 + 1280 X - 1024}}}
{{{(X-4)^4=(X-4)(X-4)(X-4)(X-4)=X^4 - 16 X^3 + 96 X^2 - 256 X + 256}}}
{{{(X-4)^3=(X-4)(X-4)(X-4)=X^3 - 12 X^2 + 48 X - 64}}}
{{{(X-4)^2=X^2-8x+16}}}


{{{X^5 - 20 X^4 + 160 X^3 - 640 X^2 + 1280 X - 1024 -7(X^4 - 16 X^3 + 96 X^2 - 256 X + 256) +7(X^3 - 12 X^2 + 48 X - 64) -7(X^2-8x+16) +7(X-4)-6}}}


{{{X^5 - 20 X^4 + 160 X^3 - 640 X^2 + 1280 X - 1024 -7X^4 + 112 X^3 - 672 X^2 + 1792 X - 1792 +7X^3 - 84X^2 + 336X - 448 -7X^2+56x-112 +7X-28-6=0}}}

{{{X^5 - 27X^4 + 279 X^3 - 1403X^2 + 3471 X - 3410=0}}}...factor

{{{X^5 -17X^4+ 109 X^3- 313 X^2 + 341X-10X^4+ 170X^3-1090 X^2+3130X -3410=0}}}...group

{{{(X^5-10X^4) -(17X^4-170X^3)+ 109X^2(X^3-10)- 313X(X-10 ) + 341(x-10)=0}}}

{{{X^4(X-10) -17X^3(X-10)+ (109X^3-1090 )- (313X^2-3130X ) + (341x-3410)=0}}}

{{{(X - 10) (X^4 - 17X^3 + 109 X^2 - 313 X + 341) = 0}}}


Real solution: {{{X =10}}}


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