Solve 3.14*x^2=81

$$3.14 \times x ^ { 2 } = 81$$

Solve for x

$$x = \frac{45 \sqrt{314}}{157} \approx 5.078993832$$

$$x = -\frac{45 \sqrt{314}}{157} \approx -5.078993832$$

Steps by Finding Square Root

Divide both sides by 3.14.

$$x^{2}=\frac{81}{3.14}$$

Expand \frac{81}{3.14} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{8100}{314}$$

Reduce the fraction \frac{8100}{314} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{4050}{157}$$

Take the square root of both sides of the equation.

$$x=\frac{45\sqrt{314}}{157} x=-\frac{45\sqrt{314}}{157}$$

Steps Using the Quadratic Formula

Divide both sides by 3.14.

$$x^{2}=\frac{81}{3.14}$$

Expand \frac{81}{3.14} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{8100}{314}$$

Reduce the fraction \frac{8100}{314} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{4050}{157}$$

Subtract \frac{4050}{157} from both sides.

$$x^{2}-\frac{4050}{157}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{4050}{157} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4050}{157}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{4050}{157}\right)}}{2}$$

Multiply -4 times -\frac{4050}{157}.

$$x=\frac{0±\sqrt{\frac{16200}{157}}}{2}$$

Take the square root of \frac{16200}{157}.

$$x=\frac{0±\frac{90\sqrt{314}}{157}}{2}$$

Now solve the equation x=\frac{0±\frac{90\sqrt{314}}{157}}{2} when ± is plus.

$$x=\frac{45\sqrt{314}}{157}$$

Now solve the equation x=\frac{0±\frac{90\sqrt{314}}{157}}{2} when ± is minus.

$$x=-\frac{45\sqrt{314}}{157}$$

The equation is now solved.

$$x=\frac{45\sqrt{314}}{157} x=-\frac{45\sqrt{314}}{157}$$