SOLUTION: The owners would like to install a wood border around a stone floor, as shown in the picture below. They have determined that the area of wood necessary is given by the polynomial

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Question 1086698: The owners would like to install a wood border around a stone floor, as shown in the picture below. They have determined that the area of wood necessary is given by the polynomial 4w2+70w, where w represents the width of the wood border. The owners can only afford 74 square feet of wood. Determine the width of the wood border. Hint: set the area of the wood equal to 74 and solve the resulting quadratic equation.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+4w%5E2+%2B+70w++=+74+
complete the square
+w%5E2+%2B+%2835%2F2%29%2Aw+=+37%2F2+
+w%5E2+%2B+%28+35%2F2+%29%2Aw+%2B+%28+35%2F4%29%5E2+=+%28+35%2F4+%29%5E2+%2B+37%2F2+
+%28+w+%2B+%2835%2F4%29+%29%5E2+=+1225%2F16+%2B+296%2F16+
+%28+w+%2B+%2835%2F4%29+%29%5E2+=+1521%2F16+
+w+%2B+35%2F4+=+39%2F4+
+w+=+1+
The width of the border is 1 ft
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check:
+4w%5E2+%2B+70w++=+74+
+4%2A1%5E2+%2B+70%2A1++=+74+
+4+%2B+70+=+74+
OK