\( 4x^2 + 70x + 300 = 504 \Rightarrow 4x^2 + 70x - 204 = 0 \)
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- Total length including path: \( 20 + 2x \), total width: \( 15 + 2x \)
- Total area: \( (20 + 2x)(15 + 2x) = 504 \)
- Expand: \( 300 + 40x + 30x + 4x^2 = 504 \)
- Divide by 2: \( 2x^2 + 35x - 102 = 0 \)
- \( x = rac{-35 \pm \sqrt{35^2 - 4(2)(-102)}}{2(2)} \)
- \( x = rac{-35 \pm \sqrt{1225 + 816}}{4} = rac{-35 \pm \sqrt{2041}}{4} \)
