Question

how to solve
$\sqrt{4} x {}^{2} = x + 2$
​

Answer 1

Answer:

➩ $x=2,-\frac{2}{3}$

Step-by-step explanation:

$\sqrt{4x^2}=x+2$

➨ We can also solve by completing both squares, however. Since we can pull out the square root.

$\sqrt{4x^2}=|2x|$ ➩ Define of Absolute Value/Square Root

➩ $\sqrt{x^2}=|x|$

Thus, our new equation is ➩ $|2x|=x+2$

To solve an absolute-value equation, let there be two conditions.

➨ Where x ≥ 0

$2x=x+2$

Move x to another side

$2x-x=2\\x=2$

➨ Where x < 0

$-2x=x+2\\-2x-x=2\\-3x=2\\x=\frac{2}{-3}\\x=-\frac{2}{3}$