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Home » Solution: Rewrite the equation by completing the square. Group $ x $ and $ y $ terms: - Dachbleche24

Solution: Rewrite the equation by completing the square. Group $ x $ and $ y $ terms: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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$ p(2) = 4a + 2b + c = 120 $
$ p(4) = 16a + 4b + c = 360 $
$ p(6) = 36a + 6b + c = 720 $
$$ (16a + 4b + c) - (4a + 2b + c) = 360 - 120 \Rightarrow 12a + 2b = 2...
Subtracting equation (2) from (3):
$$ (36a + 6b + c) - (16a + 4b + c) = 720 - 360 \Rightarrow 20a + 2b =...
Subtracting (i) from (ii):
$$ (10a + b) - (6a + b) = 180 - 120 \Rightarrow 4a = 60 \Rightarrow a...
Substitute $ a = 15 $ into (i):
$$ 6(15) + b = 120 \Rightarrow 90 + b = 120 \Rightarrow b = 30 $$

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