Question 859616
 A picture frame holds a 4in by 6 in photo.
 The frame adds a border x inches wide around three sides of the photo.
 On the fourth side the frame forms a border that is 3x-0.5 in wide.
 The combined area of photo and frame is 80.5 inē.
 Write a quadratic equation for the combined area.
:
The area of the top portion which does not include the bottom border area\
FOIL
(2x+4)(x+6) = 2x^2 + 12x + 4x + 24 = 2x^2 + 16x + 24
The area of the bottom border
(2x+4)(3x-.5) = 6x^2 - x + 12x - 2 = 6x^2 + 11x - 2
Total area = 80.5
(2x^2 + 16x + 24) + (6x^2 + 11x - 2) = 80.5
Combine like terms
2x^2 + 6x^2 + 16x + 11x + 24 - 2 - 80.5 = 0
f(x) = 8x^2 + 27x - 58.5, the quadratic equation of the combined area
:
 Then use the formula to find x.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=8, b=27, c=-58.5
{{{x = (-27 +- sqrt(27^2-4*8*-58.5 ))/(2*8) }}}
You can do the math here, I came up with reasonable answer of x=1.5"