Question 175028
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{{{x(x+1)-3(x+2)=57}}}------------------------> working eqn
where the numbers----->{{{system(x=1st,x+1=2nd,x+2=3rd)}}}
Continuing:
{{{x^2+x-3x-6-57=0}}}, distribute,expand, & put all terms to the left
{{{x^2-2x-63=0}}}
By QUadratic, where---->{{{system(a=1,b=-2,c=-63)}}}
{{{x=(-b+-sqrt(b^2-4ac))/(2a)=(-(-2)+-sqrt(-2^2-4*1*-63))/(2*1)}}}
{{{x=(2+-sqrt(4+252))/2=(2+-sqrt(256))/2=(2+-16)/2}}}
2 values:
{{{x=(2+16)/2=18/2=highlight(9)}}}----->{{{10}}},& {{{11}}}
{{{x=(2-16)/2=-14/2=highlight(-7)}}}--->{{{-6}}},& {{{-5}}}
Check by going back to the working eqn:
{{{x=9}}}
{{{9(9+1)-3(9+2)=57}}}
{{{9(10)-3(11)=57}}}
{{{90-33=57}}}
{{{57=57}}}, good
{{{x=-7}}}
{{{-7(-7+1)-3(-7+2)=57}}}
{{{-7(-6)-3(-5)=57}}}
{{{42+15=57}}}
{{{57=57}}}, good
Thank you,
Jojo</pre>