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Find all values of $x$ such that $\sqrt{4x^2} + x^2 = 6$.

 Dec 16, 2023
 #1
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\( \sqrt{4x^2} + x^2 = 6 \)

 

Assuming x is real

 

2x + x^2  = 6

 

x^2 + 2x - 6   =  0    complete the square on x

 

x^2 + 2x + 1 =  6 + 1

 

(x + 1)^2  =  7         take both roots

 

x + 1  =  ± sqrt (7)

 

x =  -1 ± sqrt (7)

 

 

cool cool cool

 Dec 16, 2023

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