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