Solve 4/5=x^2

$$\frac{ 4 }{ 5 } = { x }^{ 2 }$$

Solve for x

$$x=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

$$x=-\frac{2\sqrt{5}}{5}\approx -0.894427191$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{4}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{4}{5}$$

Subtract \frac{4}{5} from both sides.

$$x^{2}-\frac{4}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{4}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{5}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{4}{5}\right)}}{2}$$

Multiply -4 times -\frac{4}{5}.

$$x=\frac{0±\sqrt{\frac{16}{5}}}{2}$$

Take the square root of \frac{16}{5}.

$$x=\frac{0±\frac{4\sqrt{5}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{5}}{5}}{2} when ± is plus.

$$x=\frac{2\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{5}}{5}}{2} when ± is minus.

$$x=-\frac{2\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$