Question 632261
it appears you needed the quadratic equation to solve this as it could not be factored because the roots are not integers.
using the quadratic equation, you get:
x1 = 5.08276253
x2 = -7.08276253
to find the solution and to be able to use the quadratic equation, you needed to do the following:
width of the rectangle is equal to x.
the length of the rectangle is equal to the width + 3 which make the length of the rectangle equal to x+3.
if you double the length, you get 2*(x+3) which is equal to 2x+6.
if you subtract 1 from the width, you get x-1.
after you've done this, the area is equal to 66 square inches.
since the area of a rectangle is equal to length times width, this means that:
(2x+6)*(x-1)=66
that's your equation and you have to solve for x.
simplify that equation to get:
2x^2-2x+6x-6=66
combine like terms to get:
2x^2+4x-6=66
subtract 66 from both sides of that equation to get:
2x^2+4x-72=0
divide both sides of that equation by 2 to get:
x^2+2x-36=0
since this doesn't factor, you need to use the quadratic formula
since this equation is in standard form, you get:
a=1
b=2
c=-36
use the quadratic formula to get:
x1 = 5.08276253
x2 = -7.08276253
since x2 is negative, it's not a good solution because the length of any side can't be negative.
this leaves x1 = 5.08276253 as your solution.
the length of your rectangle is equal to 2x+6 which is equal to 16.16552506.
the width of your rectangle is equal to x-1 which is equal to 4.08276253
area is equal to length times width which is equal to 16.16552506 * 4.08276253 which is equal to 66.
the quadratic formula is equal to:
x = {{{(-b +-sqrt(b^2-4ac))/(2a)}}}