Solve 447=x^2

$$447 = x ^ { 2 }$$

Solve for x

$$x=\sqrt{447}\approx 21.142374512$$

$$x=-\sqrt{447}\approx -21.142374512$$

Steps by Finding Square Root

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

$$x^{2}=447$$

Take the square root of both sides of the equation.

$$x=\sqrt{447} x=-\sqrt{447}$$

Steps Using the Quadratic Formula

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

$$x^{2}=447$$

Subtract 447 from both sides.

$$x^{2}-447=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -447 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-447\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-447\right)}}{2}$$

Multiply -4 times -447.

$$x=\frac{0±\sqrt{1788}}{2}$$

Take the square root of 1788.

$$x=\frac{0±2\sqrt{447}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{447}}{2} when ± is plus.

$$x=\sqrt{447}$$

Now solve the equation x=\frac{0±2\sqrt{447}}{2} when ± is minus.

$$x=-\sqrt{447}$$

The equation is now solved.

$$x=\sqrt{447} x=-\sqrt{447}$$