2x^2+14x=88
subtract 88 from both sides
2x^2+14x-88=0
divide both sides of the equation by 2 to get x^2+7x-44=0
the equation is in the form ax^2+bx+c=0
a and b are both odd, (1 and 7)
therefore c(-44) must be factored into an odd number times an even number, NOT an even times an even
therefore you can't use 2 and 22, you must use 1 and 44 or 4 and 11(disregarding signs for the moment)
does adding 11 and 4 or subtracting 11 and 4 give you 7 ? YES, 11-4=7
-44=(4)(-11) or (-4)(11)
the coefficient of x must be +7, so you can't use 4 and -11(-11+4=-7)
you must use -4 and 11 because 11+(-4)=7
therefore you get 2(x+11)(x-4)=0
x+11=0 and x-4=0
x=-11 and x=4