Two numbers add to 18. If you square the larger number and add 6 times the smaller number you get 163. What are the numbers. Solve with quadratic equation?
x+y = 18
x^2 + 6y = 163
now substitute for y:
x^2 + 6(18-x) = 163
x^2 - 6x + 108 = 163
x^2 - 6x - 55 = 0
(x-11)(x+5) = 0
x=11 and y=7