Please help!?! The area of a shape is 95cm². Show that 2x²+6x+95=0.?
The shape kinda looks like this... and obviously not drawn accurately (and 2x+1 on the longest side, sorry it wouldn't let me write it)
__x_
l//////l
//////l
l//////L__5___
l//////////////////l x
L/////////////////l
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Overall height = H = 2x+1
Overall width = W = x+5
Cutout height = h = 2x + 1 - x = x+1
Cutout width = w = 5
Area = overall area - cutout area = 95
A = H * W - h * w = 95
A = (2x+1) (x+5) - 5 (x+1) = 95
A = 2x^2 + x + 10x + 5 - 5x - 5 = 95
A = 2x^2 + 6x = 95
A = 2x^2 + 6x - 95 = 0 <=====
Think of the region as two rectangles, the tall one on the left, and the short one of width five on the right.
The one on the left has height 2x+1 and width x; the one on the right has height x and width 5.
The sum of their areas should equal 95.
(Your formula should end up being 2x²+6x-95=0, by the way.)
(2x + 1)x + 5x = 95
2x^2 + x + 5x - 95 = 0
2x^2 + 6x - 95 = 0