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I real solutions of the equation. \[ 2 x+\sqrt{x+14}=8 \]

Ask by Ruiz Hodgson. in the United States
Jan 21,2025

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\( x=2 \)

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To solve the equation \( 2x + \sqrt{x + 14} = 8 \), start by isolating the square root: \(\sqrt{x + 14} = 8 - 2x\). Next, square both sides to eliminate the square root: \(x + 14 = (8 - 2x)^2\). This expands to \(x + 14 = 64 - 32x + 4x^2\). Rearranging terms gives the quadratic equation \(4x^2 - 33x + 50 = 0\). Use the quadratic formula to find the solutions. After solving, you will get \(x = 5\) or \(x = 2.5\). Make sure to check both solutions in the original equation, as squaring can introduce extraneous solutions!

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