Question 1103054
If you prefer to solve quadratic equations by factoring,
with {{{x}}}= average speed in traffic, in mph,
{{{2x^2-46x-391=0}}}
{{{2x^2+17x-46x-391=0}}}
{{{x(2x+17)-23(2x+17)=0}}}
{{{(x-23)(2x+17)=0}}}
The positive solution, from {{{x-23=0}}} is
{{{highlight(x=23)}}}
 
{{{391=400-9=20^2-3^2=(20+3)(20-3)=23*17}}}
To get the coefficients for the terms
{{{17x}}} and {{{-46x}}} that add up to {{{-29x}}} ,
we look for two numbers
whose product is {{{2*(-391)=-2*17*23}}} ,
and whose sum is {{{-29}}} .
{{{2*17*23=34*23}}} does not work, because {{{34-23=11}}} ,
but {{{2*17*23=17*46}}} works, because {{{46-17=29}}} .