Solve 3.14*x^2=628^2

$$3.14 \times { x }^{ 2 } = { 628 }^{ 2 }$$

Solve for x

$$x=20\sqrt{314}\approx 354.400902933$$

$$x=-20\sqrt{314}\approx -354.400902933$$

Steps by Finding Square Root

Calculate 628 to the power of 2 and get 394384.

$$3.14x^{2}=394384$$

Divide both sides by 3.14.

$$x^{2}=\frac{394384}{3.14}$$

Expand \frac{394384}{3.14} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{39438400}{314}$$

Divide 39438400 by 314 to get 125600.

$$x^{2}=125600$$

Take the square root of both sides of the equation.

$$x=20\sqrt{314} x=-20\sqrt{314}$$

Steps Using the Quadratic Formula

Calculate 628 to the power of 2 and get 394384.

$$3.14x^{2}=394384$$

Subtract 394384 from both sides.

$$3.14x^{2}-394384=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3.14 for a, 0 for b, and -394384 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3.14\left(-394384\right)}}{2\times 3.14}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3.14\left(-394384\right)}}{2\times 3.14}$$

Multiply -4 times 3.14.

$$x=\frac{0±\sqrt{-12.56\left(-394384\right)}}{2\times 3.14}$$

Multiply -12.56 times -394384.

$$x=\frac{0±\sqrt{4953463.04}}{2\times 3.14}$$

Take the square root of 4953463.04.

$$x=\frac{0±\frac{628\sqrt{314}}{5}}{2\times 3.14}$$

Multiply 2 times 3.14.

$$x=\frac{0±\frac{628\sqrt{314}}{5}}{6.28}$$

Now solve the equation x=\frac{0±\frac{628\sqrt{314}}{5}}{6.28} when ± is plus.

$$x=20\sqrt{314}$$

Now solve the equation x=\frac{0±\frac{628\sqrt{314}}{5}}{6.28} when ± is minus.

$$x=-20\sqrt{314}$$

The equation is now solved.

$$x=20\sqrt{314} x=-20\sqrt{314}$$