Solve x^2=3.14

$${ x }^{ 2 } =3.14$$

Solve for x

$$x = \frac{\sqrt{314}}{10} \approx 1.772004515$$

$$x = -\frac{\sqrt{314}}{10} \approx -1.772004515$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{314}}{10} x=-\frac{\sqrt{314}}{10}$$

Steps Using the Quadratic Formula

Subtract 3.14 from both sides.

$$x^{2}-3.14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3.14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3.14\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3.14\right)}}{2}$$

Multiply -4 times -3.14.

$$x=\frac{0±\sqrt{12.56}}{2}$$

Take the square root of 12.56.

$$x=\frac{0±\frac{\sqrt{314}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{314}}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{314}}{10}$$

Now solve the equation x=\frac{0±\frac{\sqrt{314}}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{314}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{314}}{10} x=-\frac{\sqrt{314}}{10}$$