Question 106125
If we use x and y as variables for the factors:
eq1{{{xy = 28}}}
eq2{{{x + y = 11}}}
isolate y in eq2:
{{{y = 11 - x}}}
Substitute (11-x) for y in eq1:
{{{(x)(11-x) = 28}}}
{{{11x - x^2 = 28}}}
{{{-x^2 + 11x - 28 = 0 }}}
{{{x^2 - 11x + 28 = 0 }}}
Quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (11 +- sqrt((-11)^2 - 4*1*28))/(2*1)}}}
Simplifying:
{{{x = 7 or 4}}}
Substitute values in eq2:
{{{7 + y = 11}}}
{{{y = 4}}}
{{{4 + y = 11}}}
{{{y = 7}}}
So, the two factors are 7 and 4.