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Home » Combine: \( 2x^2 + 12x + 36 = 225 \) - Londonproperty

Combine: \( 2x^2 + 12x + 36 = 225 \) - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 \[ \text{Discriminant} = 2i - 4i = -2i \]

📌 Now, compute \( \sqrt{-2i} \). Let \( \sqrt{-2i} = a + bi \), then:

📌 \[ (a + bi)^2 = a^2 - b^2 + 2abi = -2i \]

📌 \[ a^2 - b^2 = 0 \quad \text{(1)} \]

📌 \[ 2ab = -2 \quad \text{(2)} \]

📌 From (1): \( a^2 = b^2 \Rightarrow a = b \) or \( a = -b \)

📌 Try \( a = b \):

📌 Then (2): \( 2a^2 = -2 \Rightarrow a^2 = -1 \) — not possible in reals.

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