Question 658983
{{{d=sqrt((y[2]-y[1])^2+(x[2]-x[1])^2)}}}

(x, -1)=({{{x[1]+6=x+6}}},{{{y[1]+6=-1+6=-5}}})

which are 6 units from the point: means the distance is {{{6}}}

(-7, 4) =({{{x[2]}}},{{{y[2]}}})

{{{6=sqrt((4-(-1))^2+(-7-x)^2)}}}...both sides raise to the power of two

{{{6^2=(sqrt((4+1)^2+(-7-x)^2)^2)}}}

{{{36=5^2+(-7-x)^2}}}

{{{36=25+49+14x+x^2}}}

{{{36=x^2+14x+74}}}

{{{x^2+14x+74-36=0}}}

{{{x^2+14x+38=0}}}.....use quadratic formula to solve for {{{x}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-14 +- sqrt( 14^2-4*1*38 ))/(2*1) }}} 

{{{x = (-14 +- sqrt( 196-152))/2 }}} 

{{{x = (-14 +- sqrt( 44))/2 }}} 

{{{x = (-14 +- 6.6)/2 }}} 


solutions:

{{{x = (-14 + 6.6)/2 }}} 


{{{x = -7.4/2 }}} 


{{{highlight(x = -3.7)}}} 

or

{{{x = (-14 - 6.6)/2 }}} 


{{{x = -20.6/2 }}} 


{{{highlight(x = -10.3)}}} 


so, the points are (-3.7, -1) and (-7, 4)

or (-10.3, -1) and (-7, 4)


check the distance, it should be {{{6}}}:

first, the points (-3.7, -1) and (-7, 4)


{{{d=sqrt((y[2]-y[1])^2+(x[2]-x[1])^2)}}}


{{{6=sqrt((4-(-1))^2+(-7-(-3.7))^2)}}}


{{{6=sqrt((4+1)^2+(-7+3.7)^2)}}}


{{{6=sqrt(5^2+(-3.3)^2)}}}


{{{6=sqrt(25+10.89)}}}


{{{6=sqrt(35.89)}}}


{{{6=5.9908263203000635812047679131545}}}..round it to whole number


{{{6=6}}}

now, the points (-10.3, -1) and (-7, 4)


{{{d=sqrt((y[2]-y[1])^2+(x[2]-x[1])^2)}}}


{{{6=sqrt((4-(-1))^2+(-7-(-10.3))^2)}}}


{{{6=sqrt((4+1)^2+(-7+10.3)^2)}}}


{{{6=sqrt(5^2+(3.3)^2)}}}


{{{6=sqrt(25+10.89)}}}


{{{6=sqrt(35.89)}}}


{{{6=5.9908263203000635812047679131545}}}..round it to whole number


{{{6=6}}}