Solve (2/3+x)^2=19

$$( \frac { 2 } { 3 } + x ) ^ { 2 } = 19$$

Solve for x

$$x=\sqrt{19}-\frac{2}{3}\approx 3.692232277$$

$$x=-\sqrt{19}-\frac{2}{3}\approx -5.02556561$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x+\frac{2}{3}=\sqrt{19} x+\frac{2}{3}=-\sqrt{19}$$

Subtract \frac{2}{3} from both sides of the equation.

$$x+\frac{2}{3}-\frac{2}{3}=\sqrt{19}-\frac{2}{3} x+\frac{2}{3}-\frac{2}{3}=-\sqrt{19}-\frac{2}{3}$$

Subtracting \frac{2}{3} from itself leaves 0.

$$x=\sqrt{19}-\frac{2}{3} x=-\sqrt{19}-\frac{2}{3}$$