Question 166167
{{{(2x-7)^2-(x+5)^2}}} , Original eqn
expand:
{{{4x^2-28x-49-(x^2+10x+25)}}}
{{{4x^2-28x+49-x^2-10x-25}}}
{{{3x^2-38x+24}}} ---> This is simplified form
Solving for "x", by Pyth.Theorem
Given --- {{{system(a=3,b=-38,c=24)}}}
{{{x^2=(-b+-sqrt(b^2-4ac))/(2a)}}}
Plug in the values, you'll arrive for "x" --{{{system(x=12,x=2/3)}}}
Check via Original eqn:
{{{(2(12)-7)^2-(12+5)^2}}}
{{{(24-7)^2-(17)^2}}}
{{{(17)^2-289}}}
{{{289-289=0}}}
Also,
{{{(2(2/3)-7)^2-(2/3+5)^2}}}
{{{((4/3)-7)^2-(17/3)^2}}}
{{{(-17/3)^2-(17/3)^2=0}}}
Thank you,
Jojo</pre>