How to solve √(4) x {}^(2) = x + 2

Question

asked Nov 17, 2021 155k views

1 Answer

Harry Kim · Answer 1 · 2021-11-23T12:03:35+0000

Answer:

➩
x=2,-(2)/(3)

Explanation:

√(4x^2)=x+2

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

√(4x^2)=|2x| ➩ Define of Absolute Value/Square Root

➩
√(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

$-2x=x+2\\-2x-x=2\\-3x=2\\x=(2)/(-3)\\x=-(2)/(3)$