Question 1150371
*[illustration 2019121201]

x² + (x + 4)² = 20²
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x² + (x² + 8x + 16) = 400
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2x² + 8x + 16 = 400
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2(x² + 4x + 8) = 400
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x² + 4x + 8 = 200
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x² + 4x - 192 = 0
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(x - 12)(x + 16) = 0
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x = 12 and x = -16.  Since using x = -16 would give both sides negative lengths, we can throw this result out. We are left with x = 12.
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When we plug in x = 12, we can see the car travelling north has gone 12 miles, and the car travelling east has gone 16 miles.