Solve 3.14x^2*2=2

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

Solve for x

$$x=\frac{5\sqrt{314}}{157}\approx 0.564332648$$

$$x=-\frac{5\sqrt{314}}{157}\approx -0.564332648$$

Steps by Finding Square Root

Multiply 3.14 and 2 to get 6.28.

$$6.28x^{2}=2$$

Divide both sides by 6.28.

$$x^{2}=\frac{2}{6.28}$$

Expand \frac{2}{6.28} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{200}{628}$$

Reduce the fraction \frac{200}{628} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{50}{157}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{314}}{157} x=-\frac{5\sqrt{314}}{157}$$

Steps Using the Quadratic Formula

Multiply 3.14 and 2 to get 6.28.

$$6.28x^{2}=2$$

Subtract 2 from both sides.

$$6.28x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6.28 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6.28\left(-2\right)}}{2\times 6.28}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6.28\left(-2\right)}}{2\times 6.28}$$

Multiply -4 times 6.28.

$$x=\frac{0±\sqrt{-25.12\left(-2\right)}}{2\times 6.28}$$

Multiply -25.12 times -2.

$$x=\frac{0±\sqrt{50.24}}{2\times 6.28}$$

Take the square root of 50.24.

$$x=\frac{0±\frac{2\sqrt{314}}{5}}{2\times 6.28}$$

Multiply 2 times 6.28.

$$x=\frac{0±\frac{2\sqrt{314}}{5}}{12.56}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{314}}{5}}{12.56} when ± is plus.

$$x=\frac{5\sqrt{314}}{157}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{314}}{5}}{12.56} when ± is minus.

$$x=-\frac{5\sqrt{314}}{157}$$

The equation is now solved.

$$x=\frac{5\sqrt{314}}{157} x=-\frac{5\sqrt{314}}{157}$$